WB JEE 2021 | Three Dimensional Geometry Question 6 | Mathematics

WB JEE 2021

MCQ (Single Correct Answer)

-0.25

A line with positive direction cosines passes through the point P(2, $$-$$1, 2) and makes equal angle with co-ordinate axes. The line meets the plane 2x + y + z = 9 at point Q. The length of the line segment PQ equals.

1 unit

$$\sqrt 2 $$ unit

$$\sqrt 3 $$ unit

2 unit

WB JEE 2021

MCQ (Single Correct Answer)

-0.5

The plane lx + my = 0 is rotated about its line of intersection with the plane z = 0 through an angle $$\alpha$$. The equation changes to

$$lx + my \pm \tan \alpha \sqrt {{l^2} + {m^2}} = 0$$

$$lx + my \pm z\tan \alpha \sqrt {{l^2} + {m^2} + 1} = 0$$

$$lx + my \pm z\tan \alpha \sqrt {{l^2} + 1} = 0$$

$$lx + my \pm z\tan \alpha \sqrt {{l^2} + {m^2}} = 0$$

WB JEE 2020

MCQ (Single Correct Answer)

-0.25

The equation of the plane through the point $$(2, - 1, - 3)$$ and parallel to the lines

$${{x - 1} \over 2} = {{y + 2} \over 3} = {z \over { - 4}}$$ and $${x \over 2} = {{y - 1} \over { - 3}} = {{z - 2} \over 2}$$ is

$$8x + 14y + 13z + 37 = 0$$

$$8x - 14y - 13z - 37 = 0$$

$$8x - 14y - 13z + 37 = 0$$

$$x + 2y + 2z + 6 = 0$$

WB JEE 2020

MCQ (Single Correct Answer)

-0.25

The sine of the angle between the straight line $${{x - 2} \over 3} = {{y - 3} \over 4} = {{z - 4} \over 5}$$ and the plane $$2x - 2y + z = 5$$ is

$${{2\sqrt 3 } \over 5}$$

$${{\sqrt 2 } \over {10}}$$

$${4 \over {5\sqrt 2 }}$$

$${{\sqrt 5 } \over 6}$$

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