Direction vectors d1=(1,−1,1), d2=(−1,1,−1)=−d1, so lines are parallel (B). Vector joining points: (1,−3,−4). Cross product with d1 gives (−7,−5,2) with magnitude 78. Distance = 78/3=26 (D).
The two lines given by r=(i^+2j^+3k^)+μ(i^−j^+k^) and r=(2i^−j^−k^)+μ(−i^+j^−k^)
A. are perpendicular
B. are parallel.
C. have shortest distance 0.
D. have shortest distance 26.
E. have shortest distance 78.
Which of the above statements are true?
Choose the correct answer from the options given below:
Held on 16 Jul 2022 · Verified 13 Jul 2026.
A and D only
B and D only
B and C only
B and E only
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The shortest distance between the following lines: $\vec{r} = (\hat{i} + \hat{j} - \hat{k}) + s(2\hat{i} + \hat{j} + \hat{k})$ $\vec{r} = (\hat{i} + \hat{j} + 2\hat{k}) + t(4\hat{i} + 2\hat{j} + 2\hat{k})$, where s and t are scalars, is:
The angle between the line $2x = 3y = z$ and $x$- axis is:
The angle at which the line, $\frac{x-1}{0} = \frac{2-y}{-1} = \frac{2z-3}{-2}$ is inclined with the positive direction of z-axis is
$\sin^{-1}(\cos\frac{3\pi}{5})$ equals
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