The angle between the straight lines $\frac{\mathrm{x} + 1}{2} = \frac{\mathrm{y} - 2}{5} = \frac{\mathrm{z} + 3}{4}$ and $\frac{\mathrm{x} - 1}{1} = \frac{\mathrm{y} + 2}{2} = \frac{\mathrm{z} - 3}{- 3}$ is

• $45°$

• $30°$

• $60°$

• $90°$

The acute angle between the planes 2x - y + z = 6 and x + y + 2z = 3 is

• $45°$

• $60°$

• $30°$

• $90°$

The ratio in which the line joining the points (2, 4, 5) and (3, 5, - 4) is divided by the YZ-plane, is

• 2 : 3

• 3 : 2

• - 2 : 3

• 4 : - 3

A unit vector perpendicular to the plane of $\mathrm{a} = 2\hat{\mathrm{i}} - 6\hat{\mathrm{j}} - 3\hat{\mathrm{k}}$, $\mathrm{b} = 4\hat{\mathrm{i}} + 3\hat{\mathrm{j}} - \hat{\mathrm{k}}$, is

• $\frac{4\hat{\mathrm{i}} + 3\hat{\mathrm{j}} - \hat{\mathrm{k}}}{\sqrt{26}}$

• $\frac{2\hat{\mathrm{i}} - 6\hat{\mathrm{j}} - 6\hat{\mathrm{k}}}{7}$

• $\frac{3\hat{\mathrm{i}} - 2\hat{\mathrm{j}} + 6\hat{\mathrm{k}}}{7}$

• $\frac{2\hat{\mathrm{i}} - 3\hat{\mathrm{j}} - 6\hat{\mathrm{k}}}{7}$

345.

If a = $\hat{\mathrm{i}} + \hat{\mathrm{j}} + \hat{\mathrm{k}}$, b = $2\hat{\mathrm{i}} - 4\hat{\mathrm{k}}$ and c = $\hat{\mathrm{i}} + \mathrm{\lambda }\hat{\mathrm{j}} + 3\hat{\mathrm{k}}$ are coplanar, then the value of $\mathrm{\lambda }$, is

• 5/2

• 3/5

• 7/3

• None of these

The ratio rn which the XY- plane meets the line joining the points (- 3, 4, - 8)and (5, - 6, 4 ) is

• 2 : 3

• 2 : 1

• 4 : 5

• None of these

If a, b c are coplanar vectors, then which of the following is not correct ?

• $\mathrm{a} . \left(\mathrm{b} \times \mathrm{c}\right) = 0$

• $\mathrm{a} \times \left(\mathrm{b} \times \mathrm{c}\right) = 0$

• [a + b, b + c, c + a] = 0

• a = pb + qc

Find the equation of plane through the line $\frac{\mathrm{x} - 2}{2} = \frac{\mathrm{y} - 3}{3} = \frac{\mathrm{z} - 4}{5}$ and parallel to X-axis.

• 2x + 3y + 5z = 1

• 2x - 3z - 3 = 0

• 5y - 3z - 3 = 0

• 3y + 4z = 0

The value of $\text{'}\mathrm{\lambda }\text{'}$, so that the vectors $\hat{\mathrm{i}} - 3\hat{\mathrm{j}} + \hat{\mathrm{k}}$, $2\hat{\mathrm{i}} + \mathrm{\lambda }\hat{\mathrm{j}} + \hat{\mathrm{k}}$ and $3\hat{\mathrm{i}} + \hat{\mathrm{j}} - 2\hat{\mathrm{k}}$ are coplanar, will be

• 0

• 2

• $- \frac{1}{2}$

• - 4

The line passing through the point (- 1, 2 3) and perpendicular to the plane x - 2y + 3z+ 5 = 0 will be

• $\frac{\mathrm{x} + 1}{1} = \frac{\mathrm{y} - 2}{3} = \frac{\mathrm{z} - 3}{5}$

• $\frac{\mathrm{x} + 1}{1} = \frac{\mathrm{y} - 2}{3} = \frac{\mathrm{z} + 3}{3}$

• $\frac{\mathrm{x} + 1}{1} = \frac{\mathrm{y} - 2}{3} = \frac{\mathrm{z} - 3}{2}$

• $\frac{\mathrm{x} + 1}{1} = \frac{\mathrm{y} - 2}{- 2} = \frac{\mathrm{z} - 3}{3}$