The vector \(\overrightarrow{PQ}\) joining the points P(1, −1, 2) and Q(k, 1, 4) has direction ratios proportional to 3, 2, 2. The value of k is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 4
The components of \(\overrightarrow{PQ}\) are (end point) minus (starting point):
\(\overrightarrow{PQ} = (k-1)\hat{\imath}+2\hat{\jmath}+2\hat{k}\)
These components are direction ratios of \(\overrightarrow{PQ}\), so they are proportional to 3, 2, 2:
\( \displaystyle \frac{k-1}{3} = \frac{2}{2} = \frac{2}{2} \)
\(k-1 = 3\)
\(k = 4\)