Question

Find the vector equation of the line passing through the point (2, 3, −5) and making equal angles with the co-ordinate axes.

Find the vector and the Cartesian equations of a line passing through the point (1, 2, −4) and parallel to the line joining the points A(3, 3, −5) and B(1, 0, −11). Hence, find the distance between the two lines.

Find the equations of the line passing through the points A(1, 2, 3) and B(3, 5, 9). Hence, find the coordinates of the points on this line which are at a distance of 14 units from point B.

Assertion (A) : A line through the points (4, 7, 8) and (2, 3, 4) is parallel to a line through the points (−1, −2, 1) and (1, 2, 5). Reason (R) : Lines r→ = a₁→ + λb₁→ and r→ = a₂→ + μb₂→ are parallel if b₁→ · b₂→ = 0.