Find the value of 'p' for which p(\(\hat

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Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Vectors

Question:

Find the value of 'p' for which p(\(\hat{i}\)+\(\hat{j}\)+ \(\hat{k}\)) is a unit vector-

Options:

±1/√2

±1/√7

±1/√3

±1/√5

Correct Answer:

±1/√3

Explanation:

p(\(\hat{i}\)+\(\hat{j}\)+ \(\hat{k}\)) is a unit vector if |p(\(\hat{i}\)+\(\hat{j}\)+ \(\hat{k}\)) |= 1

Now, |p(\(\hat{i}\)+\(\hat{j}\)+ \(\hat{k}\)) |= 1

⇒ √(p²+p²+p²)= 1

⇒ √(3p²)= 1

⇒ √(3)p= 1

⇒ p= ±1/√3