First slide

Vectors

Question

Two vectors A and B are such that A + B = C and A ² + B² = C². If $θ$ is the angle between A and B, then the value of $θ$ is

Easy

A

$π$
B

$\frac{2 π}{3}$
C

0
D

$\frac{π}{2}$

Solution

Here, A+B = C and A²+ B²= C²
. $∴$ (A+ B)² = (C)²
IAI²+ IBI²+ 2|AI IBI cos $θ$ = ICI²
I C² I+ 2 |AI IBI cos $θ$ = I C I²
$∴$ 2|AI I BI cos $θ$ = 0
$\Rightarrow$ cos $θ$ = 0
$\Rightarrow$ $θ = \frac{π}{2}$

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