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The angle between the vector vecA and ve...

The angle between the vector `vecA` and `vecB` is `theta`. The value of the triple product `vecA.(vecBxxvecA)` is

A

Zero

B

`BA^(2) sin theta cos theta `

C

`BA^(2) cos theta `

D

`BA^(2) sin theta `

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem, we need to evaluate the triple product \( \vec{A} \cdot (\vec{B} \times \vec{A}) \). ### Step-by-Step Solution: 1. **Understanding the Triple Product**: The expression \( \vec{A} \cdot (\vec{B} \times \vec{A}) \) represents the dot product of vector \( \vec{A} \) with the cross product of vectors \( \vec{B} \) and \( \vec{A} \). 2. **Properties of the Cross Product**: The result of the cross product \( \vec{B} \times \vec{A} \) is a vector that is perpendicular to both \( \vec{B} \) and \( \vec{A} \). This means that \( \vec{A} \) and \( \vec{B} \times \vec{A} \) are orthogonal. 3. **Dot Product of Perpendicular Vectors**: The dot product of two perpendicular vectors is always zero. Therefore, since \( \vec{A} \) is perpendicular to \( \vec{B} \times \vec{A} \), we can conclude that: \[ \vec{A} \cdot (\vec{B} \times \vec{A}) = 0 \] 4. **Final Answer**: Thus, the value of the triple product \( \vec{A} \cdot (\vec{B} \times \vec{A}) \) is: \[ \boxed{0} \]
To solve the problem, we need to evaluate the triple product \( \vec{A} \cdot (\vec{B} \times \vec{A}) \). ### Step-by-Step Solution: 1. **Understanding the Triple Product**: The expression \( \vec{A} \cdot (\vec{B} \times \vec{A}) \) represents the dot product of vector \( \vec{A} \) with the cross product of vectors \( \vec{B} \) and \( \vec{A} \). 2. **Properties of the Cross Product**: The result of the cross product \( \vec{B} \times \vec{A} \) is a vector that is perpendicular to both \( \vec{B} \) and \( \vec{A} \). This means that \( \vec{A} \) and \( \vec{B} \times \vec{A} \) are orthogonal. ...
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