Q3 of 76 Page 497

Find the angle between the lines whose direction ratios are a, b, c and b – c, c – a, a – b.

Angle between the lines with direction ratios a1, b1, c1 and a2, b2, c2 is given by

Given -


a1 = a, b1 = b, c1 = c


a2 = b - c, b2 = c - a, c2 = a - b


So,


= 0


∴ cosθ = 0


So, θ = 90°


Hence, Angle between the given pair of Lines is 90°.


More from this chapter

All 76 →
1

Show that the line joining the origin to the point (2, 1, 1) is perpendicular to the line determined by the points (3, 5, –1), (4, 3, –1).

 2

If l1, m1, n1 and l2, m2, n2 are the direction cosines of two mutually perpendicular lines, show that the direction cosines of the line perpendicular to both of these are (m1n2 - m2n1), (n1l2 - n2l1), (l1m2 - l2m1)

 4

Find the equation of a line parallel to x - axis and passing through the origin.

 5

If the coordinates of the points A, B, C, D be (1, 2, 3), (4, 5, 7), (–4, 3, –6) and (2, 9, 2) respectively, then find the angle between the lines AB and CD.