Question

Show that the three lines with direction cosines

are mutually perpendicular.

Answer 1

Two lines with direction cosines, l₁, m₁, n₁ and l₂, m₂, n₂, are perpendicular to each other, if l₁l₂ + m₁m₂ + n₁n₂ = 0

(i) For the lines with direction cosines, and , we obtain

Therefore, the lines are perpendicular.

(ii) For the lines with direction cosines, and , we obtain

Therefore, the lines are perpendicular.

(iii) For the lines with direction cosines, and , we obtain

Therefore, the lines are perpendicular.

Thus, all the lines are mutually perpendicular.