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

$please see the solution below.$ $"please see the solution below."$

Explanation:

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

$a)$ $a)$

enter image source here

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

$b)$ $b)$

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

enter image source here

$12^{2} = 10^{2} + 15^{2} + 2 \cdot 10 \cdot 15 \cdot cos θ$ $12^2=10^2+15^2+2*10*15*cos theta$
$144 = 100 + 225 + 300 \cdot cos θ$ $144=100+225+300*cos theta$
$144 = 325 + 300 \cdot cos θ$ $144=325+300*cos theta$
$144 - 325 = 300 \cdot cos θ$ $144-325=300*cos theta$
$- 181 = 300 \cdot cos θ$ $-181=300*cos theta$

$cos θ = - \frac{181}{300}$ $cos theta=-181/300$

$θ = 127.11$ $theta=127.11$

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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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