R S Aggarwal Solutions for Exercise 3: EXERCISE

Show that the lines $\frac{x-3}{2}=\frac{y+1}{-3}=\frac{z-2}{4}\text{ and }\frac{x+2}{2}=\frac{y-4}{4}=\frac{z+5}{2}$  are perpendicular to each other.

If the lines $\frac{x-1}{-3}=\frac{y-2}{2\lambda }=\frac{z-3}{2}\text{ and }\frac{x-1}{3\lambda }=\frac{y-1}{1}=\frac{6-z}{5}$  are perpendicular to each other then find the value of $\lambda .$

Show that the lines $x=-y=2z and x+2=2y–1=-z+1$ are perpendicular to each other.

Find the angle between two lines whose direction ratios are

$2, 1, 2 \mathrm{and} 4, 8, 1$

Find the angle between two lines whose direction ratios are

$5, -12, 13 \mathrm{and} -3, 4, 5$

Find the angle between two lines whose direction ratios are

$1,1,2\text{ and }(\sqrt{3}-1),(-\sqrt{3}-1),4$

Find the angle between two lines whose direction ratios are

$a, b, c \mathrm{and} (b – c), (c – a), (a – b)$

If $A(1, 2, 3), B(4, 5, 7), C(-4, 3, -6) and D(2, 9, 2)$ are four given points then find the angle between the lines $AB$ and $CD.$