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Determine where aa¯ and bb¯ are orthogonal, parallel or neithe: aijka¯=2i^+3j^-k^ , bijkb¯=5i^-2j^+4k^ - Mathematics and Statistics

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Sum

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

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

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Solution

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

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

= 10 - 6 - 4 = 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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