Title 12 Maths AR Ch 11.pdf ✅

Class 12 Maths Chapter 11 Three Dimensional Geometry Assertion and Reason Questions Directions: Each of these questions contains two statements, Assertion and Reason. Each of these questions also has four alternative choices, only one of which is the correct answer. You have to select one of the codes (a), (b), (c) and (d) given below. (a) Assertion is correct, Reason is correct; Reason is a correct explanation for assertion. (b) Assertion is correct, Reason is correct; Reason is not a correct explanation for Assertion (c) Assertion is correct, Reason is incorrect (d) Assertion is incorrect, Reason is correct. 1. Assertion: If a variable line in two adjacent positions has direction cosines l, m, n, and l + δl, m + δm, n + δn, then the small angle δθ between the two positions is given by δθ = δl 2 + δm2 + δn 2 Reason: If O is the origin and A is (a, b, c), then the equation of plane through at right angle to OA is given by ax + by + cz = a 2 + b 2 + c 2 . 2. Assertion: The pair of lines given by r⃗ = iˆ − ˆj + λ(2i + k) and r⃗ = 2iˆ − kˆ + μ(i + ˆj − k) intersect. Reason: Two lines intersect each other, if they are not parallel and shortest distance = 0. 3. Consider the lines L1: x + 1 3 = y + 2 1 = z + 1 2 , L2: x − 2 2 = y − 2 2 = z − 3 3 Assertion: The distance of point (1,1,1) from the plane passing through the point (−1, −2, −1) and whose normal is perpendicular to both the lines L1 and L2 is 13 5√3 . Reason: The unit vector perpendicular to both the lines L1 and L2 is −iˆ−7jˆ+5kˆ 5√3 . 4. Assertion : Distance of a point with position vector a from a plane r.N = d is given by |a. N − d|. Reason : The length of perpendicular from origin O to the plane r.N = d is |d| |N| . 5. Consider the planes 3x − 6y − 2z = 15 and 2x + y − 2z = 5. Assertion : The parametric equations of the line of intersection of the given planes are x = 3 + 14t, y = 1 + 2t, z = 15t. Reason : The vector 14iˆ + 2jˆ + 15kˆ is parallel to the line of intersection of given planes.