Skip to content
dronacharya.ai
← JEE Main 2022 · 28 Jul · Shift 2
MathematicsSingle correct+4 / -1Question 76 of 90

JEE Main 2022 · 28 Jul · Shift 2, Mathematics question 76

A plane P is parallel to two lines whose direction ratios are −2, 1, −3 and −1, 2, −2 and it contains the point (2, 2, −2). Let P intersect the co-ordinate axes at the points A, B, C making the intercepts α\alpha, β\beta, γ\gamma. If V is the volume of the tetrahedron OABC, where O is the origin, and p=α+β+γp=\alpha+\beta+\gamma, then the ordered pair (V, p) is equal to :

Choose one option
Answer and worked solution

Official answer: B

Normal (−2,1,−3)×(−1,2,−2)=(4,−1,−3)(-2,1,-3)\times(-1,2,-2)=(4,-1,-3); plane 4x−y−3z=124x-y-3z=12.

Intercepts 3, −12, −4: p=−13p=-13, V=3×12×46=24V=\frac{3\times12\times4}6=24.

(B)

Topics:Equation of a planeScalar and vector triple products
← Previous questionNext question →