Ex. 5 Find the component form of the vector v with the given magnitude and direction angle.
a) │v│= 8 and θ = 45°
b) │w│= 24 and θ = -210°
Ex. 6 Find the direction angle of each vector to the nearest tenth of a degree.
a) v = < 3, 7 >
b) w = < -3, -8 >
Dot Product (or Scalar Product) of Vectors
If a = < a1, a2 > and b = < b1, b2 >, then a • b = _________________.
Two vectors are ______________________________ if a • b = 0.
Ex. 7 Find the dot product of u and v. Then determine if u and v are orthogonal.
a) u = < 3, -2 > and v = < -5, 1 >
b) u = < -2, -3 > and v = < 9, -6 >
Ex. 8 Find a number a so that the given vectors are orthogonal.
a) v = 3i +aj and w = i – 2j
b) v = 4i – aj and w = -2i + 5j