First slide

Vectors

Question

Vector $P = 6 \hat{i} + 4 \sqrt{2} \hat{j} + 4 \sqrt{2} \hat{k}$ makes an angle with Z-axis which is equal to

Moderate

A

$\cos^{- 1} (\frac{\sqrt{2}}{5})$
B

$\cos^{- 1} (2 \sqrt{2})$
C

$\cos^{- 1} (\frac{2 \sqrt{2}}{5})$
D

None of these

Solution

$P = 6 \hat{i} + 4 \sqrt{2} \hat{j} + 4 \sqrt{2} \hat{k}$
Let P makes angle $γ$ with Z - axis.
$∴ γ = \cos^{- 1} (\frac{P_{z}}{P})$
Here, P_z = $4 \sqrt{2}$
and $P = \sqrt{(6)^{2} + (4 \sqrt{2})^{2} + (4 \sqrt{2})^{2}} = 10$
$∴ γ = \cos^{- 1} (\frac{4 \sqrt{2}}{10}) = \cos^{- 1} (\frac{2 \sqrt{2}}{5})$

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