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Question Number 123876 Answers: 3 Comments: 0

Find the distance from the point S(1,1,5) to the line L : { ((x=1+t)),((y=3−t )),((z=2t)) :}.

$${Find}\:{the}\:{distance}\:{from}\:{the}\: \\ $$$${point}\:{S}\left(\mathrm{1},\mathrm{1},\mathrm{5}\right)\:{to}\:{the}\:{line}\: \\ $$$${L}\::\:\begin{cases}{{x}=\mathrm{1}+{t}}\\{{y}=\mathrm{3}−{t}\:}\\{{z}=\mathrm{2}{t}}\end{cases}. \\ $$

Question Number 123115 Answers: 0 Comments: 1

Σ_(n=1) ^∞ 2^n =?

$$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\mathrm{2}^{{n}} =? \\ $$

Question Number 122579 Answers: 1 Comments: 0

Question Number 120801 Answers: 1 Comments: 2

Question Number 120258 Answers: 1 Comments: 0

Question Number 118411 Answers: 1 Comments: 0

Write the vector v=(1,−2,3) as a linear combination of vectors u_1 =(1,1,1) ,u_2 =(1,2,3) and u_3 =(2,−1,1)

$${Write}\:{the}\:{vector}\:{v}=\left(\mathrm{1},−\mathrm{2},\mathrm{3}\right)\:{as}\:{a} \\ $$$${linear}\:{combination}\:{of}\:{vectors} \\ $$$${u}_{\mathrm{1}} =\left(\mathrm{1},\mathrm{1},\mathrm{1}\right)\:,{u}_{\mathrm{2}} =\left(\mathrm{1},\mathrm{2},\mathrm{3}\right)\:{and}\:{u}_{\mathrm{3}} =\left(\mathrm{2},−\mathrm{1},\mathrm{1}\right) \\ $$

Question Number 118083 Answers: 1 Comments: 0

Question Number 117543 Answers: 2 Comments: 0

If vector a^→ +b^→ +c^→ =0 ∣a^→ ∣=7, ∣b^→ ∣=3 and ∣c^→ ∣=5 find the angle vector a^→ and c^→ ?

$$\mathrm{If}\:\mathrm{vector}\:\overset{\rightarrow} {\mathrm{a}}+\overset{\rightarrow} {\mathrm{b}}+\overset{\rightarrow} {\mathrm{c}}=\mathrm{0} \\ $$$$\mid\overset{\rightarrow} {\mathrm{a}}\mid=\mathrm{7},\:\mid\overset{\rightarrow} {\mathrm{b}}\mid=\mathrm{3}\:\mathrm{and}\:\mid\overset{\rightarrow} {\mathrm{c}}\mid=\mathrm{5} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{angle}\:\mathrm{vector}\:\overset{\rightarrow} {\mathrm{a}}\:\mathrm{and}\:\overset{\rightarrow} {\mathrm{c}}\:? \\ $$

Question Number 117191 Answers: 0 Comments: 0

∫sin^(3/2) (x)dx

$$\int\mathrm{sin}^{\frac{\mathrm{3}}{\mathrm{2}}} \left(\mathrm{x}\right)\mathrm{dx} \\ $$

Question Number 115258 Answers: 1 Comments: 0

A vector of magnitude 2 along a bisector of the angle between the two vectors 2i^ −2j^ +k^ and i^ +2j^ −2k^ is __

$${A}\:{vector}\:{of}\:{magnitude}\:\mathrm{2}\:{along}\:{a}\:{bisector} \\ $$$${of}\:{the}\:{angle}\:{between}\:{the}\:{two}\:{vectors} \\ $$$$\mathrm{2}\hat {{i}}−\mathrm{2}\hat {{j}}+\hat {{k}}\:{and}\:\hat {{i}}+\mathrm{2}\hat {{j}}−\mathrm{2}\hat {{k}}\:{is}\:\_\_ \\ $$

Question Number 114975 Answers: 1 Comments: 0

.... nice mathematics.... show that :: Φ = ∫_0 ^( 1) li_2 (x)dx = (π^2 /6) −1 ✓ m.n.july.1970

$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:....\:\:{nice}\:\:{mathematics}....\: \\ $$$$ \\ $$$$\:\:\:\:\:\:\:{show}\:\:{that}\:::\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\Phi\:=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} {li}_{\mathrm{2}} \left({x}\right){dx}\:=\:\frac{\pi^{\mathrm{2}} }{\mathrm{6}}\:−\mathrm{1}\:\:\checkmark \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{m}.{n}.{july}.\mathrm{1970} \\ $$$$ \\ $$

Question Number 114808 Answers: 1 Comments: 0

...nice math... evaluate :: I =∫_0 ^( (π/4)) ((ln(1+sin(x)))/(cos(x)))dx=??? ...m.n.july.1970...

$$\:\:\:\:\:\:...{nice}\:{math}... \\ $$$$ \\ $$$$\:\:\:\:\:{evaluate}\::: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{I}\:=\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{4}}} \frac{{ln}\left(\mathrm{1}+{sin}\left({x}\right)\right)}{{cos}\left({x}\right)}{dx}=???\: \\ $$$$ \\ $$$$...{m}.{n}.{july}.\mathrm{1970}... \\ $$$$\: \\ $$

Question Number 113554 Answers: 2 Comments: 0

Using displacement vector (((−4)),((−2)) ), what is the image of ((6),(3) ) when translated?

$$\mathrm{Using}\:\mathrm{displacement}\:\mathrm{vector}\:\begin{pmatrix}{−\mathrm{4}}\\{−\mathrm{2}}\end{pmatrix}, \\ $$$$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{image}\:\mathrm{of}\:\begin{pmatrix}{\mathrm{6}}\\{\mathrm{3}}\end{pmatrix}\:\mathrm{when} \\ $$$$\mathrm{translated}? \\ $$

Question Number 111347 Answers: 0 Comments: 0

convert the plane with cartesian equation: x−3y + 2z = 7 into its vector parametric form.

$$\mathrm{convert}\:\mathrm{the}\:\mathrm{plane}\:\mathrm{with}\:\mathrm{cartesian}\:\mathrm{equation}:\:{x}−\mathrm{3}{y}\:+\:\mathrm{2}{z}\:=\:\mathrm{7} \\ $$$$\:\mathrm{into}\:\mathrm{its}\:\mathrm{vector}\:\mathrm{parametric}\:\mathrm{form}. \\ $$$$ \\ $$

Question Number 111006 Answers: 0 Comments: 2

The vectors p,q and r are mutially perpendicularwith ∣q∣=3 and ∣r∣=(√(5.4 )) .If X= 7p+5q+7r and Y=2p+3q−5r are perpendicular, find∣p∣.

$$\mathrm{The}\:\mathrm{vectors}\:\boldsymbol{\mathrm{p}},\boldsymbol{\mathrm{q}}\:\mathrm{and}\:\boldsymbol{\mathrm{r}}\:\mathrm{are}\:\mathrm{mutially}\:\mathrm{perpendicularwith} \\ $$$$\mid\boldsymbol{\mathrm{q}}\mid=\mathrm{3}\:\mathrm{and}\:\mid\boldsymbol{\mathrm{r}}\mid=\sqrt{\mathrm{5}.\mathrm{4}\:}\:.\mathrm{If}\:\mathrm{X}=\:\mathrm{7}\boldsymbol{\mathrm{p}}+\mathrm{5}\boldsymbol{\mathrm{q}}+\mathrm{7}\boldsymbol{\mathrm{r}}\:\mathrm{and} \\ $$$$\mathrm{Y}=\mathrm{2}\boldsymbol{\mathrm{p}}+\mathrm{3}\boldsymbol{\mathrm{q}}−\mathrm{5}\boldsymbol{\mathrm{r}}\:\mathrm{are}\:\mathrm{perpendicular},\:\mathrm{find}\mid\boldsymbol{\mathrm{p}}\mid. \\ $$

Question Number 108776 Answers: 1 Comments: 0

⋮^(bobhans) ∫ (dx/( (√(x(√x) −x^2 )))) = ?

$$\:\overset{{bobhans}} {\vdots} \\ $$$$\int\:\frac{{dx}}{\:\sqrt{{x}\sqrt{{x}}\:−{x}^{\mathrm{2}} }}\:=\:? \\ $$

Question Number 106340 Answers: 0 Comments: 0

Question Number 105904 Answers: 2 Comments: 0

∫ ((sin x)/(5−sin 2x)) dx ?

$$\int\:\frac{\mathrm{sin}\:{x}}{\mathrm{5}−\mathrm{sin}\:\mathrm{2}{x}}\:{dx}\:? \\ $$

Question Number 104035 Answers: 1 Comments: 0

Find the image of point OP^(→) = p^ in the line r^ =a^ +λb^ .

$${Find}\:{the}\:{image}\:{of}\:{point}\:\overset{\rightarrow} {{OP}}\:=\:\bar {{p}}\:\:{in} \\ $$$${the}\:{line}\:\:\bar {{r}}=\bar {{a}}+\lambda\bar {{b}}\:. \\ $$

Question Number 103190 Answers: 1 Comments: 0

∫_(π/4) ^(π/2) ln(ln(tan x)) dx

$$\underset{\pi/\mathrm{4}} {\overset{\pi/\mathrm{2}} {\int}}\mathrm{ln}\left(\mathrm{ln}\left(\mathrm{tan}\:{x}\right)\right)\:{dx}\: \\ $$

Question Number 101766 Answers: 0 Comments: 1

Question Number 100850 Answers: 2 Comments: 1

∫_0 ^(102) (x−1)(x−2).....(x−100)×((1/(x−1))+(1/(x−2))+...+(1/(x−100)))dx

$$\int_{\mathrm{0}} ^{\mathrm{102}} \left({x}−\mathrm{1}\right)\left({x}−\mathrm{2}\right).....\left({x}−\mathrm{100}\right)×\left(\frac{\mathrm{1}}{{x}−\mathrm{1}}+\frac{\mathrm{1}}{{x}−\mathrm{2}}+...+\frac{\mathrm{1}}{{x}−\mathrm{100}}\right){dx} \\ $$

Question Number 98408 Answers: 1 Comments: 0

Question Number 98325 Answers: 1 Comments: 0

Find the curvature vector and its magnitude at any point r^→ = (θ) of the curve r^→ = (acos θ,asin θ,aθ) .Show the locus of the feet of the ⊥ from the origin to the tangent is a curve that completely lies on the hyperbolic x^2 +y^2 −z^2 = a^2

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{curvature}\:\mathrm{vector}\:\mathrm{and} \\ $$$$\mathrm{its}\:\mathrm{magnitude}\:\mathrm{at}\:\mathrm{any}\:\mathrm{point}\: \\ $$$$\overset{\rightarrow} {\mathrm{r}}\:=\:\left(\theta\right)\:\mathrm{of}\:\mathrm{the}\:\mathrm{curve}\:\overset{\rightarrow} {\mathrm{r}}=\:\left(\mathrm{acos}\:\theta,\mathrm{asin}\:\theta,\mathrm{a}\theta\right) \\ $$$$.\mathrm{Show}\:\mathrm{the}\:\mathrm{locus}\:\mathrm{of}\:\mathrm{the}\:\mathrm{feet}\:\mathrm{of}\:\mathrm{the} \\ $$$$\bot\:\mathrm{from}\:\mathrm{the}\:\mathrm{origin}\:\mathrm{to}\:\mathrm{the}\:\mathrm{tangent}\: \\ $$$$\mathrm{is}\:\mathrm{a}\:\mathrm{curve}\:\mathrm{that}\:\mathrm{completely}\:\mathrm{lies} \\ $$$$\mathrm{on}\:\mathrm{the}\:\mathrm{hyperbolic}\:\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} −\mathrm{z}^{\mathrm{2}} =\:\mathrm{a}^{\mathrm{2}} \\ $$

Question Number 98018 Answers: 1 Comments: 0

the vector equations of two lines l_1 and l_2 are given by l_1 :r=5i−j+k+λ(−3i+2j) l_2 :r=2i+3j+2k+μ(2j+k) find thd position vdctor of intersection of thf linds l_1 and l_2 thd cartesian equatkon of the plane π, containing the lines l_(1 ) and l_2 the sine of the anhle between the plane π and the line, l_3 :r=i−5j−2k+s(2i+2j−k)

$${the}\:{vector}\:{equations}\:{of}\:{two}\:{lines}\:{l}_{\mathrm{1}} \:{and}\:{l}_{\mathrm{2}} \:{are}\:{given}\:{by} \\ $$$${l}_{\mathrm{1}} :{r}=\mathrm{5}{i}−{j}+{k}+\lambda\left(−\mathrm{3}{i}+\mathrm{2}{j}\right) \\ $$$${l}_{\mathrm{2}} :{r}=\mathrm{2}{i}+\mathrm{3}{j}+\mathrm{2}{k}+\mu\left(\mathrm{2}{j}+{k}\right) \\ $$$${find} \\ $$$${thd}\:{position}\:{vdctor}\:{of}\:{intersection}\:{of}\:{thf}\:{linds}\:{l}_{\mathrm{1}} \:{and}\:{l}_{\mathrm{2}} \: \\ $$$${thd}\:{cartesian}\:{equatkon}\:{of}\:{the}\:{plane}\:\pi,\:{containing}\:{the}\:{lines}\:{l}_{\mathrm{1}\:} {and}\:{l}_{\mathrm{2}} \\ $$$${the}\:{sine}\:{of}\:{the}\:{anhle}\:{between}\:{the}\:{plane}\:\pi\:{and}\:{the}\:{line},\:{l}_{\mathrm{3}} :{r}={i}−\mathrm{5}{j}−\mathrm{2}{k}+{s}\left(\mathrm{2}{i}+\mathrm{2}{j}−{k}\right) \\ $$

Question Number 96240 Answers: 3 Comments: 0

Find the shortest distance from the point P(2,−3,5) to the line L ((x+3)/2)=((y−1)/(−3))=((z−2)/4)

$${Find}\:{the}\:{shortest}\:{distance}\:{from}\:{the} \\ $$$${point}\:{P}\left(\mathrm{2},−\mathrm{3},\mathrm{5}\right)\:{to}\:{the}\:{line}\:{L} \\ $$$$\frac{{x}+\mathrm{3}}{\mathrm{2}}=\frac{{y}−\mathrm{1}}{−\mathrm{3}}=\frac{{z}−\mathrm{2}}{\mathrm{4}} \\ $$

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