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High School Math Calculus Precalculus with Limits: A Graphing Approach

The value of the expression v × ( v × u ) if u = 3 i − j + 4 k and v = 2 i + 2 j − k .

The value of the expression v × ( v × u ) if u = 3 i − j + 4 k and v = 2 i + 2 j − k .

Precalculus with Limits: A Graphing Approach

Precalculus with Limits: A Graphing Approach

7th Edition

ISBN: 9781305071711

Author: Ron Larson

Publisher: Brooks/Cole

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In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied unde…

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Question

Chapter 10.3, Problem 32E

To determine

To find: The value of the expression v×(v×u) if u=3i−j+4k and v=2i+2j−k .

Expert Solution & Answer

Answer to Problem 32E

The value of expression is v×(v×u)=−3i+7j+8k .

Explanation of Solution

Given information:

The given expression is v×(v×u) . The given vectors are u=3i−j+4k and v=2i+2j−k .

Calculation:

Write the formula of cross product of two vectors a=a1i+a2j+a3k and b=b1i+b2j+b3k .

a×b=|ijka1a2a3b1b2b3|

Or,

a×b=(a2b3−a3b2)i−(a1b3−a3b1)j+(a1b2−a2b1)k .

Substitute the values to calculate (v×u) in the above formula.

v×u=|ijk22−13−14|v×u=(2×4−(−1)×−1)i−(4×2−3×−1)j+(2×−1−2×3)k=7i+11j−7k .

Further use the above formula and solve to find v×(v×u) .

v×(v×u)=|ijk22−1711−7|=(−7×2−11×−1)i−(−7×2−7×−1)j+(11×2−7×2)k=−3i+7j+8k .

Therefore, the value of expression is v×(v×u)=−3i+7j+8k .

Chapter 10.3, Problem 31E

Chapter 10.3, Problem 33E

Chapter 10 Solutions

Precalculus with Limits: A Graphing Approach

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