List of top Mathematics Questions on Angle between two lines asked in CBSE Class XII

Find the angle between the following pair of lines : \( \frac{x-2}{3} = \frac{y+5}{2} = \frac{1-z}{-6} \) and \( \frac{x-7}{1} = \frac{y}{2} = \frac{6-z}{-2} \).

Find the angle between the following pair of lines :
\(\frac{x - 2}{3} = \frac{y + 5}{2} = \frac{1 - z}{-6}\) and \(\frac{x - 7}{1} = \frac{y}{2} = \frac{6 - z}{-2}\).

If the lines \(\frac{x - 3}{1} = \frac{1 - y}{1} = \frac{z + 2}{p}\) and \(\frac{2 - x}{3} = \frac{y + 1}{5} = \frac{z + 56}{2p}\) are perpendicular to each other, then find the value(s) of \(p\).

Assertion (A) : Lines given by \( x = py + q, z = ry + s \) and \( x = p'y + q', z = r'y + s' \) are perpendicular to each other when \( pp' + rr' + 1 = 0 \).
Reason (R) : Two lines \( \vec{r} = \vec{a}_1 + \lambda\vec{b}_1 \) and \( \vec{r} = \vec{a}_2 + \mu\vec{b}_2 \) are perpendicular to each other if \( \vec{b}_1 \cdot \vec{b}_2 = 0 \).

If the lines \( \frac{x - 3}{1} = \frac{1 - y}{1} = \frac{z + 2}{p} \) and \( \frac{2 - x}{3} = \frac{y + 1}{5} = \frac{z + 56}{2p} \) are perpendicular to each other, then find the value(s) of p.