class 12

Math

3D Geometry

Three Dimensional Geometry

Let L be the line of intersection of the planes $2x+3y+z=1$ and $x+3y+2z=2$. If L makes an angles $α$with the positive x-axis, then cos$α$ equals

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The radius of the circle which touches circle $(x+2)_{2}+(y−3)_{2}=25$ at point $(1,−1)$ and passes through $(4,0)$ is (a) $4$ (b) $5$ (c) $3$ (d) $8$

A line with positive direction cosines passes through the point $P(2,–1,2)$ and makes equal angles with thecoordinate axes. The line meets the plane $2x+y+z=9$ at point Q. The length of the line segment PQequals

Write the vector equation of the line passing through (1,2,3) and perpendicular to the plane $ri^+2j^ −5k^˙ +9=0.$

If a line makes an angle of $4π $with the positive directions of each of x-axis and y-axis, then the angle that the line makes with the positive direction of the z-axis is

A plane parallel to $y$-axis passing through line of intersection of planes $x+y+z=1$ & $2x+3y−z−4=0$ which of the point lie on the plane (a) $(3,2,1)$ (b) $(−3,0,1)$ (c) $(−3,1,1)$ (d) $(3,−1,1)$

if an angle between the line,and the plane,$2x−1 =1y−2 =−2z−3 $ and the plane$x−2y−kz=3$ is $3cos_{−1}(22 ) $then a value of $k$ is:

If $O$ is the origin and $P(2,3,4)$ and $Q(1,−2,1)$ be any two points, show that $OP⊥OQ$

Find the equation of the line passing through the point $P(4,6,2)$and the point of intersection of the line $3x−1 =2y =7z+1 $and the plane $x+y−z=8.$