First slide

Scalars and Vectors

Question

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

Easy

A

$\frac{π}{4} radian$
B

$\frac{π}{2} radian$
C

$\frac{3 π}{4} radian$
D

$π radian$

Solution

$\begin{array}{l} A = C \\ \tan θ = \frac{C}{A} = 1 \end{array}$
$\begin{array}{l} \Rightarrow θ = 45^{\circ} = \frac{π}{4} \\ Angle between \vec{A} and \vec{B} is \\ 180 - θ = 180^{\circ} - 45^{\circ} = 135^{\circ} = \frac{3 π}{4} ra d \end{array}$

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