If the line \(\displaystyle\frac{x-1}{2}=\frac{y+a}{3}=\frac{z-b}{-1}\) passes through the point (5, 4, 1), then the value of \(a+b\) is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 5
A point lies on the line when it makes all three ratios equal. Put (5, 4, 1) in the first ratio:
\( \displaystyle \frac{5-1}{2} = 2 \)
So the other two ratios must also equal 2:
\( \displaystyle \frac{4+a}{3} = 2 \)
\(a = 2\)
\( \displaystyle \frac{1-b}{-1} = 2 \)
\(b = 3\)
Hence \(a+b = 5\).