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Determine where aa¯ and bb¯ are orthogonal, parallel or neithe: aijka¯=-35i^+12j^+13k^ , bijkb¯=5i^+4j^+3k^ - Mathematics and Statistics

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Sum

Determine where `bar"a"` and `bar"b"` are orthogonal, parallel or neithe:

`bar"a" = -3/5hat"i" + 1/2hat"j" + 1/3hat"k"` , `bar"b" = 5hat"i" + 4hat"j" + 3hat"k"`

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Solution

`bar"a" . bar"b" = (-3/5hat"i" + 1/2hat"j" + 1/3hat"k").(5hat"i" + 4hat"j" + 3hat"k")`

`= (-3/5)(5) + (1/2)(4) + (1/3)(3)`

= -3 + 2 + 1

= 0

Since, `bar"a",bar"b"` are non-zero vectors and `bar"a".bar"b" = 0`

`bar"a"` is orthogonal to `bar"b"`

Concept: Scalar Triple Product of Vectors
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