The direction cosines of the vector {a}=(-2{i}+{j}-5{k}) are?

Correct Answer is : −230,130,−530-{2}{{30}},{1}{{30}},-{5}{{30}}−302,301,−305

-{2}{{30}},{1}{{30}},-{5}{{30}}

Correct Answer is : −230,130,−530-{2}{{30}},{1}{{30}},-{5}{{30}}−302,301,−305

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NIMCET 2017 Question Paper with solutions

Question : 97 of 120

Marks: +1, -0

\vec{a}=(-2\hat{i}+\hat{j}-5\hat{k})

are?

Solution:

Concept:

The direction cosines of the vector is the corresponding coordinate of the vector divided by the length\/Magnitude of the vector. Calculation:

Here,

\vec{a}=(-2\hat{i}+\hat{j}-5\hat{k})

|\vec{a}|=\sqrt{(-2)^2+1^2+(-5)^2}=\sqrt{30}

The direction cosines of the given vector

=\frac{-2}{\sqrt{30}},\;\frac{1}{\sqrt{30}},\;\frac{-5}{\sqrt{30}}

Hence, option (4) is correct.

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