Three Dimensional Geometry
If r=(i^+2j^+3k^)+λ(i^−j^+k^) and r=(i^+2j^+3k^)+μ(i^+j^−k^) are two lines, then the equation of acute angle bisector of two lines is
The Cartesian equations of a line are 6x−2=3y+1=2z−2. Find its direction ratios and also find a vector equation of the line.
If the line x=y=z intersect the line s∈Ax˙+s∈By˙+s∈Cz˙=2d2,s∈2Ax˙+s∈2By˙+s∈2Cz˙=d2, then find the value of 2sinA2sinB˙2sinC˙whereA,B,C are the angles of a triangle.
Find the point where line which passes through point (1,2,3) and is parallel to line r=i^+j^+2k^+λ(i^−2j^+3k^) meets the xy-plane.
Under which one of the following condition will the two planes x+y+z=7 andαx+βy+γz=3, be parallel (but not coincident)?
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