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Multivariable Calculus

8th Edition
James Stewart
ISBN: 9781305266643

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BuyFindarrow_forward

Multivariable Calculus

8th Edition
James Stewart
ISBN: 9781305266643
Textbook Problem

Use the scalar triple product to determine whether the points A(1, 3, 2), B(3, −1, 6). C(5, 2, 0), and D(3, 6, −4) lie in the same plane.

To determine

Whether the points A(1,3,2),B(3,1,6),C(5,2,0) and D(3,6,4) lie on the same plane.

Explanation

Given:

A(1,3,2),B(3,1,6),C(5,2,0) and D(3,6,4) .

Formula:

Write the expression for cross product between a and b vectors.

a×b=|ijka1a2a3b1b2b3| (1)

Write the expression for dot product between a and b vectors.

ab=a1b1+a2b2+a3b3 (2)

Scalar triple product=a(b×c)

Write the expression to find volume of the parallelepiped (V) .

V=|a(b×c)| (3)

Consider u=AB , v=AC and w=AD .

Find u=AB .

u=AB=B(3,1,6)A(1,3,2)=(31),(13),(62)=2,4,4

Find v=AC .

v=AC=C(5,2,0)A(1,3,2)=(51),(23),(02)=4,1,2

Find w=AD .

w=AD=D(3,6,4)A(1,3,2)=(31),(63),(42)=2,3,6

Modify equation (1)

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Chapter 12 Solutions

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P-48ESect-12.6 P-49ESect-12.6 P-50ESect-12.6 P-51ESect-12.6 P-52ECh-12 P-1RCCCh-12 P-2RCCCh-12 P-3RCCCh-12 P-4RCCCh-12 P-5RCCCh-12 P-6RCCCh-12 P-7RCCCh-12 P-8RCCCh-12 P-9RCCCh-12 P-10RCCCh-12 P-11RCCCh-12 P-12RCCCh-12 P-13RCCCh-12 P-14RCCCh-12 P-15RCCCh-12 P-16RCCCh-12 P-17RCCCh-12 P-18RCCCh-12 P-19RCCCh-12 P-1RQCh-12 P-2RQCh-12 P-3RQCh-12 P-4RQCh-12 P-5RQCh-12 P-6RQCh-12 P-7RQCh-12 P-8RQCh-12 P-9RQCh-12 P-10RQCh-12 P-11RQCh-12 P-12RQCh-12 P-13RQCh-12 P-14RQCh-12 P-15RQCh-12 P-16RQCh-12 P-17RQCh-12 P-18RQCh-12 P-19RQCh-12 P-20RQCh-12 P-21RQCh-12 P-22RQCh-12 P-1RECh-12 P-2RECh-12 P-3RECh-12 P-4RECh-12 P-5RECh-12 P-6RECh-12 P-7RECh-12 P-8RECh-12 P-9RECh-12 P-10RECh-12 P-11RECh-12 P-12RECh-12 P-13RECh-12 P-14RECh-12 P-15RECh-12 P-16RECh-12 P-17RECh-12 P-18RECh-12 P-19RECh-12 P-20RECh-12 P-21RECh-12 P-22RECh-12 P-23RECh-12 P-24RECh-12 P-25RECh-12 P-26RECh-12 P-27RECh-12 P-28RECh-12 P-29RECh-12 P-30RECh-12 P-31RECh-12 P-32RECh-12 P-33RECh-12 P-34RECh-12 P-35RECh-12 P-36RECh-12 P-37RECh-12 P-38RECh-12 P-1PCh-12 P-2PCh-12 P-5P

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