Three vectors A, B, and C add up to zero. Find which is false, a) vector is not zero unless vectors are parallel d) vector is not zero unless vectors are parallel c) if vectors define a plane, is in that plane d) such that
Three vectors A, B, and C add up to zero. Find which is false, a) vector is not zero unless vectors are parallel d) vector is not zero unless vectors are parallel c) if vectors define a plane, is in that plane d) such that

Answer: The correct answer is ) if vectors define a plane, is in that plane and d) such that

Given that
Now, if the vector triple product of , , and is true, then the vector will always lie on the plane that will be produced by the three variables A, B, and C, respectively. It entails  will always lie in a single plane forming sides of the triangle.
Intially take,

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$\overrightarrow{ A } \times \overrightarrow{ B }=\overrightarrow{ B } \times \overrightarrow{ C$

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Dot product with on both sides of the above equation is taken into consideration here.

$\left(\stackrel{\to }{A}×\stackrel{\to }{B}\right)·\stackrel{\to }{C}=\left(\stackrel{\to }{B}×\stackrel{\to }{C}\right)·\stackrel{\to }{C}$

Now it’s zero on two conditions. First, and are parallel. But need not be parallel to . We can use any vector perpendicular (say, P) to both and to compute the cross product. The dot product of and is also zero because the angle between them is always 90°. So is untrue.