Question

If P^Q=4i+3j+2k

Find the magnitude of PQ\ I.e[PQ]

(2) If A'=3i-j+2k and B' =2i+3j-K, find:

(1) A'×B'

(2) A'×(2A'+3B)

(3) A'.B'

Answer 1

1)

Magnitude of PQ

$|PQ|=\sqrt{4^2+3^2+2^2}=\sqrt{29}$

2)

I)$A'\times{B'}=\begin{vmatrix} i & j & k \\ 3 & -1 & 2\\ 2 & 3 & -1 \end{vmatrix}=i(1-6)-j(-3-4)+k(9-(-2))\\ =-5i+7j+11k$

I I)$A'\times (2A'+3B')\\ 2A'+3B'=2(3i-j+2k)+3(2i+3j-k)\\ 2A'+3B'=12i+7j+k\\ A'\times (2A'+3B')=\begin{vmatrix} i & j & k \\ 3 & -1 & 2\\ 12 & 7 & 1 \end{vmatrix}=i(-1-14)-j(3-24)+k(21+12)=-15i+21j+33k\\$

III)

$A'\cdot{B'}=3\cdot{2}-1\cdot{3}+2\cdot{-1}=6-3-2=1$