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Question: Answered & Verified by Expert
$\mathbf{a} \times(\mathbf{b} \times \mathbf{c})$ is equal to
MathematicsVector AlgebraJEE Main
Options:
  • A $(\mathbf{a} \cdot \mathbf{c}) \mathbf{b}-(\mathbf{a} \cdot \mathbf{a}) \mathbf{b}$
  • B $(\mathbf{a} \cdot \mathbf{c}) \mathbf{a}-(\mathbf{b} \cdot \mathbf{c}) \mathbf{a}$
  • C $(\mathbf{a} \cdot \mathbf{c}) \mathbf{b}-(\mathbf{a} \cdot \mathbf{b}) \mathbf{c}$
  • D $(\mathbf{a} \cdot \mathbf{b}) \mathbf{c}-(\mathbf{a} \cdot \mathbf{c}) \mathbf{b}$
Solution:
1452 Upvotes Verified Answer
The correct answer is: $(\mathbf{a} \cdot \mathbf{c}) \mathbf{b}-(\mathbf{a} \cdot \mathbf{b}) \mathbf{c}$
It is a fundamental concept.
(a.c)b-(a.b)c.
This is a fundamental concept of vector calculus. The vector triple product is a binary operation that takes three vectors and produces a new vector. It is also known as the cross product of a vector and a cross product.

The formula for the vector triple product is as follows:
$a \times(b \times c)=(a . c) b-(a . b) c$

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