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1. Find the volume of the parallelepiped PQRS if the vectors V(PQ), V(PR), and V(PS) are respectively 31 + 2f – k, î – 25 + 3k, and i -j + k.

1. Find the volume of the parallelepiped PQRS if the vectors V(PQ), V(PR), and V(PS) are respectively 31 + 2f – k, î – 25 + 3k, and i -j + k.

Advanced Engineering Mathematics
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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1. Find the volume of the parallelepiped PQRS if the vectors V(PQ),V(PR), and V(PS) are respectively 3î + 29 – k, î – 2j + 3k, and î - j + k. 2. Find an equation of the plane containing the point P (0, -) and the line determined by the two planes 2x – y+ z = -1 and x + 2y + z = 0. 3. Find a set of symmetric and parametric equations of the line passing through the point (1, 4, 2) intersecting the x-axis and parallel to the plane 2x + y – z + 8 = 0.
Transcribed Image Text:1. Find the volume of the parallelepiped PQRS if the vectors V(PQ),V(PR), and V(PS) are respectively 3î + 29 – k, î – 2j + 3k, and î - j + k. 2. Find an equation of the plane containing the point P (0, -) and the line determined by the two planes 2x – y+ z = -1 and x + 2y + z = 0. 3. Find a set of symmetric and parametric equations of the line passing through the point (1, 4, 2) intersecting the x-axis and parallel to the plane 2x + y – z + 8 = 0.
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