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 $(−1, −4, −2)$
✓
$(1, −2, −1)$ and $(1, 4, −2)$
D
$(1, −2, −1)$ and $(0, −6, 1)$

✓

Answer

Correct option: C.

$(1, −2, −1)$ and $(1, 4, −2)$

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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