List of top Mathematics Questions on Geometry asked in PSEB XII

Adjacent sides of a parallelogram are given by \[ \mathbf{a} = 6 \hat{i} - \hat{j} + 5 \hat{k}, \quad \mathbf{b} = \hat{i} + 5 \hat{j} - 2 \hat{k} \] Find the area of the parallelogram.

The volume of a spherical balloon is increasing at the rate of 25 c.c./s. Find the rate of change of its surface area at the instant when its radius is 5 cm.

Direction ratios of the straight line \[ \vec{r} = 4\hat{i} - 7\hat{j} + 5\hat{k} + s(9\hat{i} - 2\hat{j} + 5\hat{k}) \text{ are:} ........... \]

Find the shortest distance between the following pairs of lines: \[ \mathbf{r_1} = \hat{i} - 4 \hat{j} + 5 \hat{k} + \mu(5 \hat{i} + 9 \hat{j} + \hat{k}), \quad \mathbf{r_2} = 2 \hat{i} + 8 \hat{j} - 6 \hat{k} + \lambda(3 \hat{i} - 2 \hat{j} + \hat{k}) \]

Find the angle between the lines: \[ \mathbf{r_1} = 3 \hat{i} + 8 \hat{j} + 3 \hat{k} + \mu (\hat{i} + 2 \hat{j} - \hat{k}), \quad \mathbf{r_2} = -3 \hat{i} + 9 \hat{j} - \hat{k} + \lambda (5 \hat{i} + 3 \hat{j} + 4 \hat{k}) \]

The radius of a circle is increasing at the rate of 2 m/s. The rate of change of its circumference is: