   Chapter 11.4, Problem 34E

Chapter
Section
Textbook Problem

# Finding a Triple Scalar Product In Exercises 31-34, find u ⋅ ( v × w ) . u = 〈 1 , 1 , 1 〉 v = 〈 2 , 1 , 0 〉 w = 〈 0 , 0 , 1 〉

To determine

To calculate: The value of the triple scalar product, u(v×w), where u=<1,1,1>,v=<2,1,0> and w=<0,0,1>.

Explanation

Given:

The vectors,

u=<1,1,1>v=<2,1,0>w=<0,0,1>

Formula used:

The triple scaler product,

For the vectors given as, u=a1i+b1j+c1k,v=a2i+b2j+c2k and w=a3i+b3j+c3k,

u(v×w)=|a1b1c1a2b2c2a3b3c3|

Determinant can be calculated as,

|a1b1c1a2b2c2a3b3c3|=a1(b2c3c2b3)b1(a2c3c2a3)+c1(a2b3b2a3

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