Foot of perpendicular from origin along normal (1,1,1) is (t,t,t). Substituting in plane: 3t=3, so t=1, foot is (1,1,1). Image =2×foot−origin=(2,2,2).
Image of origin with respect to plane x+y+z=3 is:
Held on 16 Jul 2022 · Verified 13 Jul 2026.
(1,1,1)
(33,33,33)
(31,31,31)
(2,2,2)
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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
If lines $\frac{x+5}{5\lambda+2} = \frac{4-2y}{10} = \frac{1-3z}{-3}$ and $\frac{x-2}{1} = \frac{1+2y}{4\lambda} = \frac{2+z}{3}$ are perpendicular, than value of '$\lambda$' is
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