The angle between the vectors a + b and a - b | vedclass

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Question

(A) Given vectors are $a = (1, 1, 4)$ and $b = (1, -1, 4)$.First,calculate $a + b$:$a + b = (1+1, 1-1, 4+4) = (2, 0, 8)$.Next,calculate $a - b$:$a - b

Vedclass · Accepted Answer

$90$

Vedclass · Answer

(A) Given vectors are $a = (1, 1, 4)$ and $b = (1, -1, 4)$.First,calculate $a + b$:$a + b = (1+1, 1-1, 4+4) = (2, 0, 8)$.Next,calculate $a - b$:$a - b = (1-1, 1-(-1), 4-4) = (0, 2, 0)$.Now,find the dot product of $(a + b)$ and $(a - b)$:$(a + b) \cdot (a - b) = (2)(0) + (0)(2) + (8)(0) = 0 + 0 + 0 = 0$.Since the dot product of the two vectors is $0$,the vectors are perpendicular to each other.Therefore,the angle $	heta$ between them is $90^o$.

The angle between the vectors $a + b$ and $a - b$,when $a = (1, 1, 4)$ and $b = (1, -1, 4)$ is .............. $^o$

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