First slide

Scalars and Vectors

Question

For any two vectors $\vec{A}$ and $\vec{B}$ if $\vec{A} . \vec{B} = | \vec{A} \times \vec{B} |$ , the magnitude of $\vec{C} = \vec{A} + \vec{B}$ is equal to:

Moderate

A

$\sqrt{A^{2} + B^{2}}$
B

$A + B$
C

$\sqrt{A^{2} + B^{2} + \frac{A B}{\sqrt{2}}}$
D

$\sqrt{A^{2} + B^{2} + \sqrt{2} A B}$

Solution

Given $\vec{A} . \vec{B} = | \vec{A} \times \vec{B} |$
Or $A B \cos θ = A B \sin θ$
Or $\cos θ = \sin θ$
Or $θ = 45^{0}$
The magnitude of $\vec{C}$ is
$C = \sqrt{A^{2} + B^{2} + 2 A B \cos 45^{0}}$
$= \sqrt{A^{2} + B^{2} + \sqrt{2} A B}$

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