Question

If vector a=3 ,b=4 and c=5 and a+b=c find angle between a and b

Answer 1

a=3
b=4
c=5

let angle between a and b = x

The vector addition: a + b = c

$a + b = c \\ \\ \Rightarrow \sqrt{ {a}^{2} + {b}^{2} + 2ab \cos(x) } = c$

$\Rightarrow {a}^{2} + {b}^{2} + 2ab \cos(x) = {c}^{2} \\ \\ \Rightarrow {3}^{2} + {4}^{2} + 2 \times 3 \times 4 \times \cos(x) = {5}^{2}$

$\Rightarrow 9 + 16 + 24 \cos(x) = 25 \\ \\ \Rightarrow 25 + 24 \cos(x) = 25$

$\Rightarrow 24 \cos(x) = 25 - 25 = 0 \\ \\ \Rightarrow \cos(x) = 0$

$\Rightarrow \cos(x) = \cos( {90}^{o} ) \\ \\ \Rightarrow x = {90}^{o}$

Thus angle between them is 90°