The vector equation r = i − 2j − k + t(6j − k) represents a strai… - Vidyadip

MCQ

The vector equation r = i − 2j − k + t(6j − k) represents a straight line passing through the points:

A
(0, 6, −1) and (1, −2, −1)
B
(0, 6, −1) and (−1, −4, −2)
C
(1, −2, −1) and (1, 4, −2)
D
(1, −2, −1) and (0, −6, 1)

✓

Answer

(1, −2, −1) and (1, 4, −2)

Solution:

Cartesian representation of the given line is,

$\frac{\text{x}-1}{0}=\frac{\text{y}+2}{6}=\frac{\text{z}+1}{-1}=\text{t}$

So any point on the given line is of the form (1, 6t − 2, − t − 1) where t can be any real numbers

So for t = 0 and 1 the corresponding points are (1, −2, −1) and (1, 4, −2)

You can check other options does not satisfy above point for any t.

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