# Determine where aa¯ and bb¯ are orthogonal, parallel or neithe: aijka¯=4i^-j^+6k^ , bijkb¯=5i^-2j^+4k^ - Mathematics and Statistics

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"

#### 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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