Angle Between Two Vectors and Vector Scalar Product

Angle Between Two Vectors and Vector Scalar Product This is a worked example problem that shows how to find the angle between two vectors. The angle between vectors is used when finding the scalar product and vector product. The scalar product is also called the dot product or the inner product. Its found by finding the component of one vector in the same direction as the other and then multiplying it by the magnitude of the other vector. Vector Problem Find the angle between the two vectors: A 2i 3j 4kB i - 2j 3k Solution Write the components of each vector. Ax 2; Bx 1Ay 3; By -2Az 4; Bz 3 The scalar product of two vectors is given by: A Â · B A B cos ÃŽ ¸ |A||B| cos ÃŽ ¸ or by: A Â · B AxBx AyBy AzBz When you set the two equations equal and rearrange the terms you find: cos ÃŽ ¸ (AxBx AyBy AzBz) / AB For this problem: AxBx AyBy AzBz (2)(1) (3)(-2) (4)(3) 8 A (22 32 42)1/2 (29)1/2 B (12 (-2)2 32)1/2 (14)1/2 cos ÃŽ ¸ 8 / [(29)1/2 * (14)1/2] 0.397 ÃŽ ¸ 66.6Â °