Find the direction cosines of the vector

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Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Vectors

Question:

Find the direction cosines of the vector (5\(\hat{i}\) + \(\hat{j}\)+ 2\(\hat{k}\))

Options:

-(5/ √30, 1/√30, 2/√30)

(5/ √30, 1/√30, 2/√30)

(5/ √30, 2/√30, 2/√30)

(5/ √30, 1/√30, 5/√30)

Correct Answer:

(5/ √30, 1/√30, 2/√30)

Explanation:

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

magnitude of (\(\vec{a}\)) =√(5)² +(1)² +(2)² = √30

Hence the direction cosines are =(5/ √30, 1/√30, 2/√30)