Three Dimensional Geometry
The equation of a plane which is perpendicular to (2i^−3j^+k^) and at a distance of 5 units from the origin is?
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Find the equation of a line which passes through the point (1,1,1)
and intersects the lines 2x−1=3y−2=4z−3and1x+2=2y−3=4z+1˙
Distance of the point P(p) from the line r=a+λb is a. ∣∣(a−p)+∣∣b∣∣2((p−a)b˙)b∣∣ b. ∣∣(b−p)+∣∣b∣∣2((p−a)b˙)b∣∣ c. ∣∣(a−p)+∣∣b∣∣2((p−b)b˙)b∣∣ 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=
Show that the lines α−δx−a+d=αy−a=α+δz−a−d
What is the angle between the planes2x−y+z=6 andx+y+2z=3?
The locus of a point, such that the sum of the squares of its distances from the planes x+y+z=0,x−z=0 And x−2y+z=0is 9, is
If Q is the image of the point P(2, 3, 4) under the reflection in the plane x−2y+5z=6, then the equation of the line PQis
Find the equation of the plane passing through the line 5x−1=6y+2=4z−3 and point (4,3,7)˙