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