If A¯=2i^−3j^+4k^then choose the correct options among the following

The component of A ¯ in xz plane is 20 , The component of A ¯ in xy plane is 16

If A¯=2i^−3j^+4k^then choose the correct options among the following

A ¯ = 2 i ^ − 3 j ^ + 4 k ^ i A x y = − 3 2 + 2 2 = 9 + 4 = 13 i i A x z = 2 2 + 4 2 = 20 i i i A x y = 2 2 + − 3 2 = 13 i v cos α = A x A ¯ = 2 2 2 + − 3 2 + 4 2 = 2 4 + 9 + 16 = 2 29 ∴ α = cos − 1 2 29

The component of A ¯ in xz plane is 20

The component of A ¯ in xy plane is 16

The component of A ¯ in xy plane is 13

The angle made by vectors A ¯ with x axis is equal to cos − 1 2 29

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If $\bar{A} = 2 \hat{i} - 3 \hat{j} + 4 \hat{k}$ then choose the correct options among the following

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The component of $\bar{A}$ in xz plane is $\sqrt{20}$

The component of $\bar{A}$ in xy plane is $\sqrt{16}$

The component of $\bar{A}$ in xy plane is $\sqrt{13}$

The angle made by vectors $\bar{A}$ with x axis is equal to $\cos^{- 1} \frac{2}{\sqrt{29}}$

answer is A, B.

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Detailed Solution

$\bar{A} = 2 \hat{i} - 3 \hat{j} + 4 \hat{k} (i) A_{x y} = \sqrt{{(- 3)}^{2} + {(2)}^{2}} = \sqrt{9 + 4} = \sqrt{13} (i i) A_{x z} = \sqrt{2^{2} + 4^{2}} = \sqrt{20} (i i i) A_{x y} = \sqrt{2^{2} + {(- 3)}^{2}} = \sqrt{13} (i v) \cos α = \frac{A_{x}}{|\bar{A}|} = \frac{2}{\sqrt{2^{2} + {(- 3)}^{2} + {(4)}^{2}}} = \frac{2}{\sqrt{4 + 9 + 16}} = \frac{2}{\sqrt{29}} ∴ α = \cos^{- 1} (\frac{2}{\sqrt{29}})$

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