How do you find the angle between the vectors $u = 5 i + 5 j$ $u=5i+5j$ and $v = - 8 i + 8 j$ $v=-8i+8j$ ?

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Answer 1 · 2016-07-14T11:05:49

Angle: $90°$

In order to calculate the angle between two vectors, we have to know that

$cos(theta) = (vecu * vecv)/(||vecu|| ||vecv||)$

$u * v$ means the dot product of $u$ and $v$ , which we can calculate using the formula

$vecu*vecv = u_1 v_1 + u_2 v_2 + ... u_n v_n$

In our case, $vecu = 5hati + 5hatj$ and $vecv = -8hati + 8hatj$

$vecu * vecv = 5(-8) + 5(8) = -40 + 40 = 0$

Since the dot product is $0$ , we can conclude that $vecu$ and $vecv$ are perpendicular to each other, so the angle between them would equal $90$ .

How do you find the angle between the vectors u=5i+5ju=5i+5ju=5i+5j and v=-8i+8jv=−8i+8jv=-8i+8j?