Question

A student tries to tie ropes, parallel to each other from one end of the wall to the other. If one rope is along the vector $3\hat{i} + 15\hat{j} + 6\hat{k}$ and the other is along the vector $2\hat{i} + 10\hat{j} + \hat{k}$, then the value of $\lambda$ is :

• A. 6
• B. 1
• C. 4
• D. 1/4

Hint:

To find the value of $\lambda$, compute the magnitudes of the two vectors and take their ratio.

Answer 1

The Correct Option is B

The scalar $\lambda$ is determined by the ratio of the vector magnitudes: \[ \lambda = \frac{\text{Magnitude of first vector}}{\text{Magnitude of second vector}} = \frac{\sqrt{3^2 + 15^2 + 6^2}}{\sqrt{2^2 + 10^2 + 1^2}} = 1 \] Consequently, option $(B)$ is the correct selection.