8. A line e is parallel to the vector 2i- 2j + k and passes through the point A with position vector 9i - 5j + 2k. A plane with its normal parallel to the vector 3i – 4j – k passes through a point with position vector -i+ 4k. (a) Obtain vector equation of the plane. (b) Find the position vector of the point B which lies on the plane and the line AB is a hormal to the plane. c) Determine the position vector of the point of intersection between line l and the plane.

8. A line e is parallel to the vector 2i- 2j + k and passes through the point A with position vector 9i - 5j + 2k. A plane with its normal parallel to the vector 3i – 4j – k passes through a point with position vector -i+ 4k. (a) Obtain vector equation of the plane. (b) Find the position vector of the point B which lies on the plane and the line AB is a hormal to the plane. c) Determine the position vector of the point of intersection between line l and the plane.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

8. A line e is parallel to the vector 2i-2j + k and passes through the point A with
position vector 9i -5j + 2k. A plane with its normal parallel to the vector
3i – 4j – k passes through a point with position vector -i+ 4k.
(a) Obtain vector equation of the plane.
(b) Find the position vector of the point B which lies on the plane and the line AB is a
normal to the plane.
(c) Determine the position vector of the point of intersection between line l and the plane.
(d) Find the unit vector which is perpendicular to both vectors 2i - 2j +k and
-i + 4k.

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