First slide

Vectors

Question

If A=4i-2j+6k and B=i-2j-3k, the angle which the A + B makes with X-axis is

Moderate

A

$\cos^{- 1} (3 / \sqrt{50})$
B

$\cos^{- 1} (5 / \sqrt{50})$
C

$\cos^{- 1} (4 / \sqrt{50})$
D

$\cos^{- 1} (12 / \sqrt{50})$

Solution

A+B=5i-4j+3k
and $| A + B | = \sqrt{{(25) + (16) + 9}}$
(A+B).i=5 $\sqrt{2}$
or $| A + B | \cos θ = 5$
$\begin{array}{lrl} ∴ \sqrt{50} \cos θ = 5 \\ or θ = \cos^{- 1} (5 / \sqrt{50}) = 45^{0} \end{array}$

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