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If → a = 4 ^ I + 3 ^ J + ^ K and → B = ^ I − 2 ^ K , Then Find ∣ ∣ 2 ^ B × → a ∣ ∣ . - Mathematics

Sum
\[\text{ If }  \vec{a} = 4 \hat{ i }  + 3 \hat{ j }  + \hat{ k }  \text{ and }  \vec{b} = \hat{ i }  - 2 \hat{ k } ,\text{  then find }  \left| 2 \hat{ b } \times \vec{a} \right| .\]

 

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Solution

\[\text{ Given } : \]

\[ \vec{a} = 4 \hat{ i }  + 3 \hat{ j }  + \hat{ k }  \]

\[2 \vec{b} = 2 \hat{ i  }+ 0 \hat{ j } - 4 \hat{ k } \]

\[2 \vec{b} \times \vec{a} = \begin{vmatrix}\hat{ i } & \hat{ j }  & \hat{ k } \\ 2 & 0 & - 4 \\ 4 & 3 & 1\end{vmatrix}\]

\[ = \left( 0 + 12 \right) \hat{ i }  - \left( 2 + 16 \right) \hat { j } + \left( 6 - 0 \right) \hat{ k }  \]

\[ = 12 \hat{ i } - 18 \hat{ j }  + 6 \hat{ k }  \]

\[ \Rightarrow \left| 2 \vec{b} \times \vec{a} \right| = \sqrt{{12}^2 + \left( - {18}^2 \right) + 6^2}\]

\[ = \sqrt{504}\]

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APPEARS IN

RD Sharma Class 12 Maths
Chapter 25 Vector or Cross Product
Exercise 25.1 | Q 5 | Page 29
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