Three Dimensional Geometry
The Cartesian equation of a line are 2x−2=3y+1=−2z−3. What is its vector equation?
If θ is the acute angle between the diagonals of a cube, then which one of the following is correct?
The centre of the circle given by ri^+2j^+2k^˙=15and∣∣r−(j^+2k^)∣∣=4 is a. (0,1,2) b. (1,3,5) c. (−1,3,4) d. none of these
Let A(a⃗ ) and B(b⃗ ) be points on two skew line r⃗ =a⃗ +λ⃗ and r⃗ =b⃗ +uq⃗ and the shortest distance between the skew line is 1, where p⃗ and q⃗ are unit vectors forming adjacent sides of a parallelogram enclosing an area of 12units. If an angle between AB and the line of shortest distance is 60∘, then AB=
A plane passes through a fixed point (a,b,c)˙ Show that the locus of the foot of the perpendicular to it from the origin is the sphere x2+y2+z2−ax−by−cz=0.
The point of intersecting of the line passing through (0,0,1) and intersecting the lines x+2y+z=1,−x+y−2z=2andx+y=2,x+z=2 with xy-plane is