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Vectors, Dot Products and Orthogonality

3. Two vectors Xand Y are said to be orthogonal (perpendicular) if the angle between them is r/2.
(a) Prove that X and V are orthogonal if and only if X . Y = 0.
Use part (a) to determine if the following vectors are orthogonal.
(b) X =(?6,4.2) and Y =(6,5,8)
(c) X=(?4,8,3) and Y=(2,5,16)
(d) X = (?5. 7, 2) and Y = (4, 1, 6)
(e) Find two different vectors that are orthogonal to X = (1, 2, ?5).

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Vectors, Dot Products and Orthogonality are investigated. The solution is detailed and well presented.

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