Question:
The scalar $\overrightarrow{A}.[(\overrightarrow{B}+\overrightarrow{C})\times(\overrightarrow{A}+\overrightarrow{B}+\overrightarrow{C})]$ eqy=ual
The scalar $\overrightarrow{A}.[(\overrightarrow{B}+\overrightarrow{C})\times(\overrightarrow{A}+\overrightarrow{B}+\overrightarrow{C})]$ eqy=ual
Updated On: June 02, 2025
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- $[\overrightarrow{A}.\overrightarrow{B}\overrightarrow{C}]+[\overrightarrow{B}.\overrightarrow{C}\overrightarrow{A}]$
- $[\overrightarrow{A}.\overrightarrow{B}\overrightarrow{C}]$
- None of these
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The Correct Option is A
Solution and Explanation
$\overrightarrow{A}.\{(\overrightarrow{B}+\overrightarrow{B})\times(\overrightarrow{A}+\overrightarrow{B}+\overrightarrow{C})$
$[\because\text{it is a scalar triple product of three vectors of the form } \overrightarrow{A},\overrightarrow{B}+\overrightarrow{C},\overrightarrow{A}+\overrightarrow{B}+\overrightarrow{C}]$
$=\overrightarrow{A}(\overrightarrow{B}\times\overrightarrow{A}+\overrightarrow{B}\times\overrightarrow{B}+\overrightarrow{B}\times\overrightarrow{C}+\overrightarrow{C}\times\overrightarrow{A}+\overrightarrow{C}\times\overrightarrow{B}+\overrightarrow{C}\times\overrightarrow{C})$
$=\overrightarrow{A}.(\overrightarrow{B}\times\overrightarrow{A}+\overrightarrow{A}.(\overrightarrow{B}\times\overrightarrow{C})+\overrightarrow{A}.(\overrightarrow{C}\times\overrightarrow{B})$
$[\overrightarrow{A}\overrightarrow{B}\overrightarrow{A}]-[\overrightarrow{A}\overrightarrow{B}\overrightarrow{C}]=0$
$[\because\text{it is a scalar triple product of three vectors of the form } \overrightarrow{A},\overrightarrow{B}+\overrightarrow{C},\overrightarrow{A}+\overrightarrow{B}+\overrightarrow{C}]$
$=\overrightarrow{A}(\overrightarrow{B}\times\overrightarrow{A}+\overrightarrow{B}\times\overrightarrow{B}+\overrightarrow{B}\times\overrightarrow{C}+\overrightarrow{C}\times\overrightarrow{A}+\overrightarrow{C}\times\overrightarrow{B}+\overrightarrow{C}\times\overrightarrow{C})$
$=\overrightarrow{A}.(\overrightarrow{B}\times\overrightarrow{A}+\overrightarrow{A}.(\overrightarrow{B}\times\overrightarrow{C})+\overrightarrow{A}.(\overrightarrow{C}\times\overrightarrow{B})$
$[\overrightarrow{A}\overrightarrow{B}\overrightarrow{A}]-[\overrightarrow{A}\overrightarrow{B}\overrightarrow{C}]=0$
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Vector Algebra
A vector is an object which has both magnitudes and direction. It is usually represented by an arrow which shows the direction(→) and its length shows the magnitude. The arrow which indicates the vector has an arrowhead and its opposite end is the tail. It is denoted as
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