2021-06-08

Vector A = 5i +1j and vector B = 2i -6j +2k
What is the cross product of $A×B$,
find the x component?
Find the y component?
Find the z component?

funblogC

$\stackrel{\to }{A}=5\stackrel{^}{i}+1\stackrel{^}{j}$
$\stackrel{\to }{B}=2\stackrel{^}{i}-6\stackrel{^}{j}+2\stackrel{^}{k}$
The cross product of both the vector is,
$\stackrel{\to }{A}×\stackrel{\to }{B}=\left[\begin{array}{ccc}\stackrel{^}{i}& \stackrel{^}{j}& \stackrel{^}{k}\\ 5& 1& 0\\ 2& -6& 2\end{array}\right]$
$\stackrel{\to }{A}×\stackrel{\to }{B}=\left[\left(2×1\right)-\left(-6×0\right)\right]\stackrel{^}{i}+\left[\left(2×0\right)-\left(5×2\right)\right]\stackrel{^}{j}+\left[\left(-6×5\right)-\left(2×1\right)\right]$
Solving of the expression
$\stackrel{\to }{A}×\stackrel{\to }{B}=2\stackrel{\to }{i}-10\stackrel{\to }{j}-32\stackrel{\to }{k}$
The x-component is 2
The y-component is -10
The z-component is -32

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