Question

The straight line given by the equation \[ \vec r=(4\hat{i}+5\hat{j}+\hat{k})+s(4\hat{i}+6\hat{j}+2\hat{k}) \] is coplanar with the straight line given below. Choose the correct option.

• A. \(\vec r=(\hat{i}-2\hat{j}+3\hat{k})+p(2\hat{i}+3\hat{j}-4\hat{k})\)
• B. \(\vec r=(3\hat{i}-4\hat{j}+3\hat{k})+q(-4\hat{i}+5\hat{j}-6\hat{k})\)
• C. \(\vec r=(2\hat{i}+5\hat{j}-4\hat{k})+r(\hat{i}+4\hat{j}-3\hat{k})\)
• D. \(\vec r=(-4\hat{i}+4\hat{j}+4\hat{k})+t(7\hat{i}+5\hat{j})\)

Hint:

Two lines are coplanar if \[ (\vec a_2-\vec a_1)\cdot(\vec b_1\times\vec b_2)=0. \] This is the standard scalar triple product test for coplanarity.

Answer 1

The Correct Option is D