Class 12

Math

3D Geometry

Three Dimensional Geometry

Find the equation of the plane passing through the origin and parallel to the plane $5x−3y+7z+13=0$.

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L1 and L2 are two lines whose vector equations are L1:r⃗ =λ((cosθ+3√)i^+(2√sinθ)j^+(cosθ−3√)k^)L2:r⃗ =μ(ai^+bj^+ck^), where λ and μ are scalars and α is the acute angle between L1 andL2. If the angle ′α′ is independent of θ then the value of ′α′ is

Two spheres of radii 3 and 4 cut orthogonally The radius of common circle is

Find the equation of a line which passes through the point $(2,3,4)$ and which has equal intercepts on the axes.

A plane passing through (1, 1, 1) cuts positive direction of coordinate axes at A, B and C, then the volume of tetrahedron OABC satisfies

The angle between the line x−2a=y−2b=z−2c and the plane ax+by+cz+6=0 is

The d. r. of normal to the plane through (1, 0, 0), (0, 1, 0) which makes an angle π/4 with plane x+y=3 are

The line joining the points $(−2,1,−8)and(a,b,c)$ is parallel to the line whose direction ratios are $6,2,and3.$ Find the values of $a,bandc$

From a point P(λ,λ,λ), perpendiculars PQ and PR are drawn, respectively, on the lines y=x, z=1 and y=−x, z=−1. If ∠QPR is a right angle, then the possible value(s) of λ is/are