List of top Mathematics Questions on Vector Algebra asked in PSEB XII

Find the value of \( p \) if the vectors \( \vec{p} \hat{i} - 8 \hat{j} + 5 \hat{k} \) and \( 5 \hat{i} + 2 \hat{j} - 3 \hat{k} \) are perpendicular to each other.

Find the area of the triangle whose sides are given by vectors: \[ \vec{a} = 2\hat{i} + 3\hat{j} - \hat{k}, \quad \vec{b} = \hat{i} - \hat{j} + 3\hat{k} \]

Vector equation of the line \( \frac{x - 5}{4} = \frac{y - 3}{5} = \frac{z + 3}{-8} \) is:

If \( \vec{a} \) is a non-zero vector then \( |\vec{a} \times \vec{a}| \) is equal to:

Adjacent sides of a parallelogram are given by \( 6\hat{i} - \hat{j} + 5\hat{k} \) and \( \hat{i} + 5\hat{j} - 2\hat{k} \). Find the area of parallelogram.

Prove that for any two non-zero vectors \( \vec{a} \) and \( \vec{b} \), \( |\vec{a} + \vec{b}| \leq |\vec{a}| + |\vec{b}| \). Also write the name of this inequality.

Find the value of \( p \) if the vectors \( p\hat{i} - 8\hat{j} + 5\hat{k} \) and \( 5\hat{i} + 2\hat{j} - 3\hat{k} \) are perpendicular to each other.

If \( \vec{a} \) is a non-zero vector then \( |\vec{a} \times \vec{a}| \) is equal to:

Name of the inequality \( |\vec{a} \cdot \vec{b}| \le |\vec{a}| |\vec{b}| \) is: