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Question
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"`.
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