Question

Two vectors are given by a = 3.51+ 2.6j and b = 3.11+ 4.7. Find (a) a x b (b) a b , (c) a + b b , and (d) the component of a along the direction of b ?

just need help with part d answers to a, b, c are 8.39, 23.07, 54.77

Answer 1

d)

$\hat{b}$ = unit vector along the direction of $\underset{b}{\rightarrow}$ = (3.1 i + 4.7 j) /(sqrt(3.1² + 4.7²)) = (3.1 i + 4.7 j) /5.63

magnitude of component vector of A along $\hat{b}$ is given as

|$\underset{a}{\rightarrow}$| = $\underset{a}{\rightarrow}$ . $\hat{b}$ = (3.5 i + 2.6 j) ((3.1 i + 4.7 j) /5.63) = 4.1

components of $\underset{a}{\rightarrow}$ along $\hat{b}$ is given as

|$\underset{a}{\rightarrow}$| $\hat{b}$ = (4.1) ((3.1 i + 4.7 j) /5.63) = 2.3 i + 3.4 j