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Determine where aa¯ and bb¯ are orthogonal, parallel or neithe: aijka¯=4i^-j^+6k^ , 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" = 4hat"i" - hat"j" + 6hat"k"` , `bar"b" = 5hat"i" - 2hat"j" + 4hat"k"`

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Solution

`bar"a" . bar"b" = (4hat"i" - hat"j" + 6hat"k").(5hat"i" - 2hat"j" + 4hat"k")`

`= (4)(5) + (- 1)(- 2) + (6)(4)`

= 20 + 2 + 24

= 46 ≠ 0 

`therefore bar"a"` is not orthogonal to `bar"b"`

It is clear that `bar"a"` is not a scalar multiple of `bar"b"`

`bar"a"` is not parallel to `bar"b"`

Hence, `bar"a"` is neither parallel nor orthogonal to `bar"b"`.

Concept: Scalar Triple Product of Vectors
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