Trigonometric EquationHard
Question
A line with direction cosines proportional to 2, 1, 2 meets each of the lines x = y + a = z and x + a = 2y = 2z. The co-ordinates of each of the point of intersection are given by
Options
A.(3a, 3a, 3a), (a, a, a)
B.(3a, 2a, 3a), (a, a, a)
C.(3a, 2a, 3a), (a, a, 2a)
D.(2a, 3a, 3a), (2a, a, a)
Solution
Any point on the line 
= t1 (say) is (t1, t1 - a, t1) and any point on the line
= t2 (say) is (2t2 - a, t2, t2).
Now direction cosine of the lines intersecting the above lines is proportional to
(2t2 - a - t1, t2 - t1 + a, t2 - t1).
Hence 2t1 - a - t1 = 2k, t2 - t1 + a = k and t2 - t1 = 2k
On solving these, we get t1 = 3a , t2 = a.
Hence points are (3a, 2a, 3a) and (a, a, a).
= t1 (say) is (t1, t1 - a, t1) and any point on the line = t2 (say) is (2t2 - a, t2, t2).Now direction cosine of the lines intersecting the above lines is proportional to
(2t2 - a - t1, t2 - t1 + a, t2 - t1).
Hence 2t1 - a - t1 = 2k, t2 - t1 + a = k and t2 - t1 = 2k
On solving these, we get t1 = 3a , t2 = a.
Hence points are (3a, 2a, 3a) and (a, a, a).
Create a free account to view solution
View Solution FreeMore Trigonometric Equation Questions
The number of values of x in [0, 5π] satisfying the equation 3cos2x − 10cosx + 7 = 0 are-...If x1, x2, x3, x4 are roots of the equation x4 - x3 sin 2β + x2 cos 2β -x cos β - sin β = 0, then ta...If 0 ≤ x ≤ 2π, 0 ≤ y ≤ 2π and sin x + sin y = 2 then the value of x + y is-...For x ∈ (0, π) the equation sinx + 2sin2x - sin3x = 3 has...A ray passing through (2, -3) is incident parallel to x-axis on a mirror lying along x2 - 4x + 8y + 12 = 0. Which of the...