K. C. Sinha and Abhishek Chandra Solutions for Exercise 2: EXERCISE

The direction cosines of the ray from $(0, 0, 0)$ to $(2, -3, 6)$ are

Two lines with direction cosines $l_1, m_1, n_1$ and $l_2, m_2, n_2$ are at right angles if

The projections of the segment $PQ$ on the coordinate axes are $-9, 12, -8$, respectively. The direction cosines of the line $PQ$ are

If the direction cosines of a line are $\frac{1}{c}, \frac{1}{c}, \frac{1}{c}$, then

A line making angles ${45}^{\circ }$ and ${60}^{\circ }$ with the positive direction of the $x$ and $y$-axes respectively, makes with the positive direction of $z$-axis an angle of

The angle formed between a line with direction ratio $2:2:1$ and a line joining $(3,1,4)$ to $(7,2,12)$ is

The direction cosines of a line equally inclined to the positive directions of axes are

If a line makes angles $\alpha , \beta , \gamma$ with the axes, then $\cos 2\alpha +\cos 2\beta +\cos 2\gamma =$