Mathegoras

Vectors and matrices › Lines, planes and vectors in space › Angles between vectors and planes

Cosine of angle with orthogonal vector sum

High school · ●●○○○ 20 pts

Let a,\mathbf{a}, b,\mathbf{b}, c\mathbf{c} be three vectors with equal magnitudes, such that any two of them are orthogonal. If θ\theta is the angle between a\mathbf{a} and a+b+c,\mathbf{a} + \mathbf{b} + \mathbf{c}, find cos⁡θ.\cos \theta. Round to two decimal places.

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dot productvector magnitudeangle between vectorsorthogonal vectors