Andhra Pradesh Board Solutions for Chapter: Direction Cosines and Direction Ratios, Exercise 1: Exercise 6(a)

A line makes angles $90°, 60°$ and $30°$ with the positive directions of $X, Y, Z-$axes respectively. Find its direction cosines.

If a line makes angles $\alpha , \beta , \gamma$ with the positive directions of $X, Y, Z-$axes, what is the value of ${\sin }^2\alpha +{\sin }^2\beta +{\sin }^2\gamma$?

If $P(\sqrt{3},1,2\sqrt{3})$ is a point in space, find direction cosines of $OP$.

Find the direction cosines of the line joining the points $(-4,1,7)$ and $(2,-3,2)$.

Find the direction cosines of the sides of the triangle whose vertices are $(3,5,-4), (-1,1,2)$ and $(-5,-5,-2)$.

Show that the lines $PQ$ and $RS$ are parallel where $P,Q,R,S$ are the points $(2,3,4), (4,7,8), (-1,-2,1)$ and $(1,2,5)$ respectively.

Find the direction cosines of two lines which are connected by the relations $l-5m+3n=0$ and $7l^2+5m^2-3n^2=0$.