First slide

Vectors

Question

The direction cosines of vector (A - B), if $A = 2 \hat{i} + 3 \hat{j} + \hat{k}, B = 2 \hat{i} + 2 \hat{j} + 3 \hat{k}$ are

Moderate

A

$0, \frac{1}{\sqrt{5}}, \frac{- 2}{\sqrt{5}}$
B

$0, \frac{2}{\sqrt{5}}, \frac{1}{\sqrt{5}}$
C

$0, 0, \frac{1}{\sqrt{5}}$
D

None of these

Solution

We have $A - B = \hat{j} - 2 \hat{k} = C$
$C = \sqrt{1 + 4} = \sqrt{5}$
$\cos α = \frac{0}{\sqrt{5}} = 0, \cos β = \frac{1}{\sqrt{5}} and \cos γ = \frac{- 2}{\sqrt{5}}$

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