Let a 1 x + b 1 y + c 1 z + d 1 = 0 and a 2 x + b 2 y + c 2 z + d 2 = 0 be two planes…
Mathematics · JEE Advanced · NTA Exams — Three Dimensional Geometry
Let a1x + b1y + c1z + d1 = 0 and a2x + b2y + c2z + d2 = 0 be two planes, where d1, d2 > 0 . Then origin lies in acute angle if a1a2 + b1b2 + c1c2 < 0 and origin lies in obtuse angle if a1a2 + b1 b2 + c1c2 > 0 .
Further point (x1, y1, z1) and origin both lie either in acute angle or in obtuse angle, if (a1x1 + b1y1 + c1z1 + d1)
(a2x1 + b2y1 + c2z1 + d2) > 0 . One of (x1, y1, z1) and origin lie in acute angle and the other in obtuse angle, if
(a1x1 + b1y1 + c1z1 + d1) (a2x1 + b2y1 + c2z1 + d2) < 0
Given the planes 2x + 3y – 4z + 7 = 0 and
x – 2y + 3z – 5 = 0, if a point P is (1, –2, 3), then
- O and P both lie in acute angle between the planes
- O and P both lie in obtuse angle
- O lies in acute angle, P lies in obtuse angle
- O lies in obtuse angle, P lies an acute angle.
Answer
(B) O and P both lie in obtuse angle
Sign up free on Edukali to view the step-by-step worked solution and practice thousands of similar questions.
Related practice questions
- The straight lines x-1 1 = y-2 2 = z-3 3 and x-1 2 = y-2 2 = z-3 -2 are
- If a ~b lie on a plane normal to the plane containing c ~d then, ( a b ) ( c d ) is equal to
- The length of the projection of the line segment joining the points (5, –1, 4) and (4, –1, 3) on the plane x…
- The vectors p q satisfy the system of equations 2 p + q = a , p +2 q = b and the angle between p q is θ. If…
- If a plane cuts off intercepts OA = a, OB = b, OC = c from the coordinate axes, then the area of the triangle…
- Three vectors a , b and c are such that a b = c , b c = a , c a = b . Answer the following questions …
- The equation of a plane passing through the line of intersection of the planes x + 2 y + 3 z = 2 and x – y +…
- Let p is the p.v. of the orthocentre & g is the p.v. of the centroid of the triangle ABC where circumcentre…
More Three Dimensional Geometry questions · Browse all practice questions