Three Dimensional Geometry
Find the acute angle between the following planes.
x+y−z=4 and x+2y+z=9.
If α,β,andγ are the an gles which a directed line makes with the positive directions of the co-ordinates axes, then find the value of sin2α+sin2β+sin2γ˙
Determine whether the following pair of lines intersect or not. (1) r=i^−5j^+λ(2i^+k^);r=2i^−j^+μ(i^+j^−k^) (2) r=i^+j^−k^+λ(3i^−j^);r=4i^−k^+μ(2i^+3k^)
Find the equation the plane which contain the line of intersection of the planesri^+2j^+3k^˙−4=0andr2i^+j^−k^˙+5=0 and which is perpendicular to the plane r(5i^+3j^−6k^)+8=0 .
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
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˙