First slide

Vectors

Question

Given that A + B = C and that C is perpendicular to A. Further, if |A| = |C|, then what is the angle between A and B?

Moderate

A

$\frac{π}{4}$
B

$\frac{π}{2}$
C

$\frac{3 π}{4}$
D

$π$

Solution

From the figure, B cos $θ$ = C …(i)
and B sin $θ$ = A …(ii)

Given, IAI = I CI
$∴$ IB cos $θ$ | = IB sin $θ$ | or $θ$ = 45⁰
Hence, angle between A and B is 135⁰ or $\frac{3 π}{4}$

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