Problem : Find a vector which is perpendicular to both u = (3, 0, 2) and v = (1, 1, 1).The vector u×v is perpendicular to both u and v, so we need only compute the cross product to do this problem. From the component formula, u×v = (- 2, - 1, 3). Using the dot product we can check that this vector is indeed perpendicular to u and v.
Problem : A triangle has two sides of length 5 and 6. If the triangle's area is 12, what is the angle between these two sides?
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