   Chapter 12.4, Problem 38E

Chapter
Section
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

Modify equation (1)

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