Question

Given the vectors r = 3i - 2j + 5k and s = -2i - j + 2k(a) Find r x s(b) Find the magnitude of r x s

Answer 1

(a) r x s = i + 4j + k

(b) The magnitude of r x s is √18

Step-by-step explanation

Given vectors:

r = 3i - 2j + 5k

s = -2i - j + 2k

Step-by-step solution:

(a) Find r x s

`\begin{gathered} r* s=\begin{bmatrix}{i} & {j} & {k} \\ {3} & {-2} & {5} \\ {2} & {-1} & {2}\end{bmatrix}=i\begin{bmatrix}{-2} & {5} \\ {-1} & {2}\end{bmatrix}-j\begin{bmatrix}{3} & {5} \\ {2} & {2}\end{bmatrix}+k\begin{bmatrix}{3} & {-2} \\ {2} & -{1}\end{bmatrix} \\ =i((-2*2)-(5*-1))-j((3*2)-(5*2))+k((3*-1)-(-2*2)) \\ \\ =i(-4+5)-j(6-10)+k(-3+4) \\ \\ =i+4j+k \end{gathered}`

Therefore, r x s = i + 4j + k

(b) Find the magnitude of r x s

`\lvert{r* s}\rvert=\lvert{i+4j+k}\rvert=√(1^2+4^2+1^2)=√(1+16+1)=√(18)`

Hence, the magnitude of r x s is √18