What is the cross product of $[3, 1, - 5]$ $[3,1,-5]$ and $[2, - 1, 1]$ $[2, -1, 1]$ ?

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What is the cross product of $[3, 1, - 5]$ $[3,1,-5]$ and $[2, - 1, 1]$ $[2, -1, 1]$ ?

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Answer 1 · 2016-05-12T21:29:16

$A X B = - 4 i - 13 j - 5 k$ $AXB=-4i-13j-5k$

Explanation:

$\to A = [3, 1, - 5]$ $vec A=[3,1,-5]$

$\to B = [2, - 1, 1]$ $vec B=[2,-1,1]$

$A_{x} = 3$ $A_x=3$
$A_{y} = 1$ $A_y=1$
$A_{z} = - 5$ $A_z=-5$

$B_{x} = 2$ $B_x=2$
$B_{y} = - 1$ $B_y=-1$
$B_{z} = 1$ $B_z=1$

$A X B = (A_{y} \cdot B_{z} - A_{z} \cdot B_{y}) i - (A_{x} \cdot B_{z} - A_{z} \cdot B_{x}) j + (A_{x} \cdot B_{y} - A_{y} - B_{x}) k$ $AXB=(A_y*B_z-A_z*B_y)i-(A_x*B_z-A_z*B_x)j+(A_x*B_y-A_y-B_x)k$

$A X B = i (1 \cdot 1 - (5 \cdot 1)) - j (3 \cdot 1 + 2 \cdot 5) + k (- 1 \cdot 3 - 2 \cdot 1)$ $AXB=i(1*1-(5*1))-j(3*1+2*5)+k(-1*3-2*1)$

$A X B = i (1 - 5) - j (3 + 10) + k (- 3 - 2)$ $AXB=i(1-5)-j(3+10)+k(-3-2)$

$A X B = - 4 i - 13 j - 5 k$ $AXB=-4i-13j-5k$

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What is the cross product of $[3, 1, - 5]$ $[3,1,-5]$ and $[2, - 1, 1]$ $[2, -1, 1]$ ?

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Explanation:

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What is the cross product of $[3, 1, - 5]$ $[3,1,-5]$ and $[2, - 1, 1]$ $[2, -1, 1]$ ?