Three Dimensional Geometry
Show that the following pairs of planes are at right angles.
x−2y+4z=10 and 18x+17y+4z=49.
A line makes angles, θ,ϕ and ψ with x, y, z axes respectively. Consider the following:1.sin2θ+sin2ϕ=cos2ψ2. cos2θ+cos2ϕ=sin2ψ3.sin2θ+cos2ϕ=cos2ψWhich of the above is/are correct?
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
A line passes through the points (6,−7,−1)and(2,−3,1)˙ Find te direction cosines off the line if the line makes an acute angle with the positive direction of the x-axis.