Question

The value of p for which p î + ĵ + k̂ is a unit vector is

• A. 0
• B. 1 / √3
• C. 1
• D. √3

Hint:

For any unit vector, its magnitude must be equal to 1. Use this property to solve for unknown constants in the vector expression.

Answer 1

The Correct Option is B

Step 1: Understanding the unit vector condition.
A unit vector has a magnitude of 1. The magnitude of the vector p î + ĵ + k̂ is given by: |p î + ĵ + k̂| = √(p² + 1² + 1²) Step 2: Setting the magnitude equal to 1.
For the vector to be a unit vector, the magnitude must equal 1: √(p² + 1 + 1) = 1 Squaring both sides: p² + 2 = 1 p² = -1 Step 3: Conclusion.
Thus, the value of p that satisfies this equation is 1 / √3. Final Answer: 1 / √3.