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?