17. Triple vector products The triple vector products (u X v) X w and u X (v X w) are usually not equal, although the formulas for evaluating them from components are similar: (u X v) X w = (u •w)v – (v• w)u. u X (v X w) = (u•w)v – (u • v)w. (u• v)w. Verify each formula for the following vectors by evaluating its two sides and comparing the results. u a. 2i 2j 2k b. i - j+ k c. 2i + j d. i +j – 2k 2i + j – 2k -i + 2j – k 2i – j + k i + 2k -i - k 2i + 4j – 2k

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.2: Direct Methods For Solving Linear Systems
Problem 51EQ
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17. Triple vector products The triple vector products (u X v) X w
and u X (v X w) are usually not equal, although the formulas for
evaluating them from components are similar:
(u X v) X w = (u •w)v – (v• w)u.
u X (v X w) = (u•w)v – (u • v)w.
(u• v)w.
Verify each formula for the following vectors by evaluating its two
sides and comparing the results.
u
a. 2i
2j
2k
b. i - j+ k
c. 2i + j
d. i +j – 2k
2i + j – 2k
-i + 2j – k
2i – j + k
i + 2k
-i - k
2i + 4j – 2k
Transcribed Image Text:17. Triple vector products The triple vector products (u X v) X w and u X (v X w) are usually not equal, although the formulas for evaluating them from components are similar: (u X v) X w = (u •w)v – (v• w)u. u X (v X w) = (u•w)v – (u • v)w. (u• v)w. Verify each formula for the following vectors by evaluating its two sides and comparing the results. u a. 2i 2j 2k b. i - j+ k c. 2i + j d. i +j – 2k 2i + j – 2k -i + 2j – k 2i – j + k i + 2k -i - k 2i + 4j – 2k
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