If the angle between the vectors c =ai+2j and d=3i+j is 45° , find the two possible values of a


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Question Number 190811 by otchereabdullai last updated on 12/Apr/23

$I f t h e a n g l e b e t w e e n t h e v e c t o r s$ $c = a i + 2 j a n d d = 3 i + j i s 45 °, f i n d$ $t h e t w o p o s s i b l e v a l u e s o f a$
	Answered by safojontoshtemirov last updated on 12/Apr/23

	$c = (a; 2) d = (3; 1)$ $c d =∣ c ∣∣ d ∣ c o s a$ $3 a + 2 = \sqrt{a^{2} + 4} \cdot \sqrt{5}$ $9 a^{2} + 12 a + 4 = 5 a^{2} + 20$ $4 a^{2} + 12 a - 16 = 0$ $a^{2} + 3 a - 4 = 0$ $a = - 4 a = 1$
	Commented by otchereabdullai last updated on 12/Apr/23

	$G o d b l e s s y o u s i r!$
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