Maths-
General
Easy

Question

# Suppose the direction cosines of two lines are given by al+bm+cn=0 and fmn+gln+hlm=0 where f, g, h, a, b, c are arbitrary constants and l, m, n are direction cosines of the lines. On the basis of the above information answer the following The given lines will be perpendicular if

Hint:

### We are aware that the direction cosine is equal to the cosine of the angle formed by the line intersecting each of the three coordinate axes, namely the x, y, and z axes. If the angles subtended by these three axes are α, β, and γ, then the direction cosines are cos α, cos β, cos γ respectively.We know that distance of (x, y,z) from origin is r: x2 + y2 + z2 = r2So: l2 + m2 + n2  = 1Now that we have given: al+bm+cn=0 and fmn+gnl+hlm=0. Canceling n, we get:

We define lines using cosine ratios of the line. While working with three-dimensional geometry (used in so many applications such as game designing), it is needed to express the importance of the line present in 3-D space. Here we were asked to find the condition for perpendicular line, so it is .