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Determine where aa¯ and bb¯ are orthogonal, parallel or neithe: aijka¯=-9i^+6j^+15k^ , bijkb¯=6i^-4j^-10k^ - Mathematics and Statistics

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Sum

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

`bar"a" = - 9hat"i" + 6hat"j" + 15hat"k"` , `bar"b" = 6hat"i" - 4hat"j" - 10hat"k"`

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Solution

`bar"a" = - 9hat"i" + 6hat"j" + 15hat"k" = - 3(3hat"i" - 2hat"j" - 5hat"k")`

`= - 3/2 (6hat"i" - 4hat"j" - 19hat"k")`

∴ `bar"a" = - 3/2 bar"b"`

i.e. `bar"a"` is a non-zero scalar multiple of `bar"b"`

Hence, `bar"a"` is parallel to `bar"b"`

Concept: Scalar Triple Product of Vectors
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