Question

If the magnitude of the vector \(\vec{P} = x\hat{i} + 0.8\hat{j} + 0.6\hat{k}\) is 2, then the value of x is.

• A. $\sqrt{5}$
• B. 2
• C. 3
• D. $\sqrt{3}$
• E. $\sqrt{2}$

Hint:

For a unit vector, the sum of squares of components is 1.

Answer 1

The Correct Option is D

Step 1: Concept
Magnitude of a vector $\vec{P} = A\hat{i} + B\hat{j} + C\hat{k}$ is $|\vec{P}| = \sqrt{A^2 + B^2 + C^2}$.

Step 2: Meaning
The sum of squares of the components equals the square of the magnitude.

Step 3: Analysis
$x^2 + (0.8)^2 + (0.6)^2 = 2^2 \Rightarrow x^2 + 0.64 + 0.36 = 4$.
$x^2 + 1 = 4 \Rightarrow x^2 = 3 \Rightarrow x = \sqrt{3}$.

Step 4: Conclusion
Hence, the value of x is $\sqrt{3}$.
Final Answer: (D)