MHT CET 2020 19th October Evening Shift | Three Dimensional Geometry Question 206 | Mathematics

The equation of the line passing through $(1,2,3)$ and perpendicular to the lines $x-1=\frac{y+2}{2}=\frac{z+4}{4}$ and $\frac{x-1}{2}=\frac{y-2}{2}=z+3$ is

$x-1=\frac{y-2}{2}=\frac{z-3}{4}$

$\frac{x-1}{4}=\frac{2-y}{5}=\frac{z-3}{2}$

$\frac{x-1}{6}=\frac{y-2}{7}=\frac{z-3}{2}$

$\frac{x-1}{6}=\frac{2-y}{7}=\frac{z-3}{2}$

MHT CET 2020 16th October Evening Shift

MCQ (Single Correct Answer)

-0

If the plane $$2 x+3 y+5 z=1$$ intersects the co-ordinate axes at the points $$A, B, C$$, then the centroid of $$\triangle A B C$$ is

$$(2,3,5)$$

$$\left(\frac{1}{6}, \frac{1}{9}, \frac{1}{15}\right)$$

$$\left(\frac{3}{2}, 1, \frac{3}{5}\right)$$

$$\left(\frac{1}{2}, \frac{1}{3}, \frac{1}{5}\right)$$

MHT CET 2020 16th October Evening Shift

MCQ (Single Correct Answer)

-0

The direction co-sines of the line which bisects the angle between positive direction of $$Y$$ and $$Z$$ axes are

$$0, \frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}$$

$$\frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}, 0$$

$$\frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}$$

$$\frac{1}{\sqrt{2}}, 0, \frac{1}{\sqrt{2}}$$

MHT CET 2020 16th October Evening Shift

MCQ (Single Correct Answer)

-0

The angle between the lines $$\frac{x-1}{4}=\frac{y-3}{1}=\frac{z}{8}$$ and $$\frac{x-2}{2}=\frac{y+1}{2}=\frac{z-4}{1}$$ is

$$\cos ^{-1}\left(\frac{2}{3}\right)$$

$$\cos ^{-1}\left(\frac{1}{2}\right)$$

$$\cos ^{-1}\left(\frac{3}{4}\right)$$

$$\cos ^{-1}\left(\frac{1}{3}\right)$$

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