Vectors, EXT1* V1 2021 HSC 11c

Find the angle between the vectors `underset~a = ((2),(0),(4))` and `underset~b = ((-3),(1),(2))`, giving the angle in degrees correct to 1 decimal place. (3 marks)

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`83.1^@`

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`underset~a = ((2),(0),(4)) \ , \ |underset~a| \ = sqrt{2^2 + 4^2} = sqrt20`

`underset~b = ((-3),(1),(2)) \ , \ |underset~b| \ = sqrt{(-3)^2 + 1^2 + 2^2} = sqrt14`

`underset~a * underset~b`	`= ((2),(0),(4)) ((-3),(1),(2)) = – 6 + 0 + 8 = 2`
`underset~a * underset~b`	`= \|underset~a\| \|underset~b\| \ cos theta`
`2`	`= sqrt20 sqrt14 \ cos theta`
`cos theta`	`= 2/sqrt280`
`theta`	`= cos^(-1) (1/sqrt70)`
	`= 83.1^@ \ text{(1 d.p,)}`