Find direction cosines of vector -2-3k-

The correct option is D (1√(14), 2√(14), 3√(14)) Let w⃗ =î +2ĵ +3k̂ #10; #10; #10;Direction cosines of the vector are #160; #10; #10; ...

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Standard XII

Mathematics

Basic Inverse Trigonometric Functions

Find directio...

Question

Find direction cosines of vector $^i + 2^j + 3^k$ .

(\frac{1}{14}, \frac{2}{14}, \frac{3}{14})

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(\sqrt{14}, \frac{\sqrt{14}}{2}, \frac{\sqrt{14}}{3})

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(- \frac{1}{\sqrt{14}}, - \frac{2}{\sqrt{14}}, - \frac{3}{14})

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(\frac{1}{\sqrt{14}}, \frac{2}{\sqrt{14}}, \frac{3}{\sqrt{14}})

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Solution

The correct option is D $(\frac{1}{\sqrt{14}}, \frac{2}{\sqrt{14}}, \frac{3}{\sqrt{14}})$
Let $\to w =^i + 2^j + 3^k$

Direction cosines of the vector are

$⎛ ⎜ ⎜ ⎝ \frac{1}{\sqrt{{(1)}^{2} + {(2)}^{3} + {(3)}^{2}}}, \frac{2}{\sqrt{{(1)}^{2} + {(2)}^{3} + {(3)}^{2}}}, \frac{3}{\sqrt{{(1)}^{2} + {(2)}^{3} + {(3)}^{2}}} ⎞ ⎟ ⎟ ⎠$
$= (\frac{1}{\sqrt{14}}, \frac{2}{\sqrt{14}}, \frac{3}{\sqrt{14}})$

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Find direction cosines of vector ^i+2^j+3^k.

The correct option is D (1√14,2√14,3√14)Let →w=^i+2^j+3^k Direction cosines of the vector are ⎛⎜ ⎜⎝1√(1)2+(2)3+(3)2,2√(1)2+(2)3+(3)2,3√(1)2+(2)3+(3)2⎞⎟ ⎟⎠=(1√14,2√14,3√14)

Find direction cosines of vector $^i + 2^j + 3^k$ .