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Home Vectors Product of Vectors Examples Example 7: Test for Perpendiculars and Parallels
 
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Example 7: Test for Perpendiculars and Parallels

Test for A ⊥ B and A ∥ B using the inner product. (Figure 10.4.3 illustrates this example.)

(a)

A = 3i + j - k. B = i - 3j + k. We compute A · B and |A| |B|.

A · B = -1, |A| |B| = 11. Since A · B ≠ 0, not A ⊥ B. Since A · B ≠ ± |A| |B|, not A ∥ B

 10_vectors-151.gif
(b)

A = 2i - √3j + k, B = -√8i + √6j - √2k.

A · B = -8√2, |A| |B| = 8√2. Therefore A ∥ B.

 10_vectors-152.gif
(c) A = 3i + j - k, B = i - 3j. A · B = 0. Therefore A ⊥ B. 10_vectors-153.gif
    Figure 10.4.3

Home Vectors Product of Vectors Examples Example 7: Test for Perpendiculars and Parallels

Last Update: 2006-11-15