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Let a, b, c be three vectors that lie on the same line. Find ​

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Let  a, b, c  be three vectors that lie on the same line. Find $$\mathbf{a} \times \mathbf{b} + \mathbf{b} \times \mathbf{c} + \mathbf{c} \times \mathbf{a}.$$

Apr 9, 2022

#1
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The vectors is $(1,0,0)$.

Apr 9, 2022
#2
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If two vectors are parallel, their cross product (vector product ) is zero.

So, all three products are zero in which case their sum will be zero.

Apr 11, 2022