Let L 1 and L 2 be the following straight lines. L_ 1 : x-1 1 = y -1 = z-1 3 and L_ 2 …
Mathematics · JEE Advanced · NTA Exams — Co-ordinate Geometry
Let L1 and L2 be the following straight lines.
\(L_{1}: \frac{x-1}{1}=\frac{y}{-1}=\frac{z-1}{3} \text { and } L_{2}: \frac{x-1}{-3}=\frac{y}{-1}=\frac{z-1}{1} .\)
Suppose the straight line \(L: \frac{x-\alpha}{l}=\frac{y-1}{m}=\frac{z-\gamma}{-2}\) lies in the plane containing L1 and L2, and passes through the point of intersection of L1 and L2. If the line L bisects the acute angle between the lines L1 and L2, then which of the following statements is/are TRUE?
\(L_{1}: \frac{x-1}{1}=\frac{y}{-1}=\frac{z-1}{3} \text { and } L_{2}: \frac{x-1}{-3}=\frac{y}{-1}=\frac{z-1}{1} .\)
Suppose the straight line \(L: \frac{x-\alpha}{l}=\frac{y-1}{m}=\frac{z-\gamma}{-2}\) lies in the plane containing L1 and L2, and passes through the point of intersection of L1 and L2. If the line L bisects the acute angle between the lines L1 and L2, then which of the following statements is/are TRUE?
- a − g = 3
- l + m = 2
- a − g = 1
- l + m = 0
Answer
(B) l + m = 2
Sign up free on Edukali to view the step-by-step worked solution and practice thousands of similar questions.
Related practice questions
- From the point A(0, 3) on the circle x² + 4x + (y – 3)² = 0, a chord AB is drawn & extended to a point M such…
- Consider the straight line ax + by = c, where a, b, c ∈ R + this line meets the coordinate axes at A and B…
- Tangent are drawn from the points on the line x – y – 5 = 0 to x 2 + 4y 2 = 4, then all the chords of contact…
- If P, Q, R are three co-normal points on the parabola y 2 = 4ax then the centroid of the triangle PQR always…
- The graph of the function cos x cos (x + 2) – cos 2 (x + 1) is
- Match the items of Column I with those of Column II. The correct matching is :
- The triangle formed by the tangent to the curve f ( x ) = x 2 + bx – b at the point (1, 1) and the coordinate…
- Let g ( x ) be a function defined on [–1, 1]. If the area of the equilateral triangle with two of its…
More Co-ordinate Geometry questions · Browse all practice questions