Find the angle between two vectors, 10 and 15 units long, when their resultant is (a) 20 units long and (b) 12 units long. Draw the appropriate figure?

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Find the angle between two vectors, 10 and 15 units long, when their resultant is (a) 20 units long and (b) 12 units long. Draw the appropriate figure?

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Answer 1 · 2017-12-30T11:15:26

$"please see the solution below."$

Explanation:

$"you can use the cosine theorem to solve this problem."$
$c^2=a^2+b^2+2*a*b*cos theta$
$"where;"$

$a)$

enter image source here

$c=20$
$a=10$
$b=15$
$20^2=10^2+15^2+2*10*15*cos theta$
$400=100+225+300*cos theta$
$400=325+300*cos theta$
$400-325=300*cos theta$
$75=300*cos theta$
$cos theta=75/300=1/4$
$theta =75.52 " deg"$

$b)$

$a=10$
$b=15$
$c=12$

enter image source here

$12^2=10^2+15^2+2*10*15*cos theta$
$144=100+225+300*cos theta$
$144=325+300*cos theta$
$144-325=300*cos theta$
$-181=300*cos theta$

$cos theta=-181/300$

$theta=127.11$

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Find the angle between two vectors, 10 and 15 units long, when their resultant is (a) 20 units long and (b) 12 units long. Draw the appropriate figure?

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Explanation:

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