Answer to Question #221664 in Mechanics | Relativity for Sam 63x

Question #221664

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'


1
Expert's answer
2021-08-02T03:24:01-0400

1)

Magnitude of PQ

PQ=42+32+22=29|PQ|=\sqrt{4^2+3^2+2^2}=\sqrt{29}

2)

I)A×B=ijk312231=i(16)j(34)+k(9(2))=5i+7j+11kA'\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×(2A+3B)2A+3B=2(3ij+2k)+3(2i+3jk)2A+3B=12i+7j+kA×(2A+3B)=ijk3121271=i(114)j(324)+k(21+12)=15i+21j+33kA'\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)

AB=3213+21=632=1A'\cdot{B'}=3\cdot{2}-1\cdot{3}+2\cdot{-1}=6-3-2=1


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