Vectors and matrices › Vectors in the plane › Components and addition

Angles of a unit vector with the axes

High school · ●●○○○ 20 pts

A unit vector a⃗\vec a makes an angle π3\frac{\pi}{3} with i^\hat i, an angle π4\frac{\pi}{4} with j^\hat j, and an acute angle θ\theta with k^\hat k. Find θ\theta in degrees, and hence find the components of a⃗\vec a along i^\hat i, j^\hat j, k^\hat k, in that order. Round the second component to two decimal places.

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direction cosinesunit vectorsangle between vectorsvector components