First slide

Scalars and Vectors

Question

If the vectors $(\hat{i} + \hat{j} + \hat{k})$ and $3 \hat{i}$ form two sides of a triangle, the area of the triangle is

Moderate

A

$\sqrt{3} u n i t$
B

$2 \sqrt{3} u n i t$
C

$\frac{3}{\sqrt{2}} u n i t$
D

$3 \sqrt{2} u n i t$

Solution

: Area of triangle = $\frac{1}{2} A B \sin θ = \frac{| A \times B |}{2}$
$A \times B = (\hat{i} + \hat{j} + \hat{k}) \times 3 \hat{i}$
$= - 3 \hat{k} + 3 \hat{j}$
$| A \times B | = \sqrt{(- 3)^{2} + (3)^{2}}$
$= 3 \sqrt{2}$
Area = $\frac{3 \sqrt{2}}{2} = \frac{3}{\sqrt{2}} u n i t$

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