# Find → a . ( → B × → C ) , If → a = 2 ^ I + ^ J + 3 ^ K , → B = − ^ I + 2 ^ J + ^ K and → C = 3 ^ I + ^ J + 2 ^ K . - Mathematics

Short Note
Sum

Find $\vec{a} . \left( \vec{b} \times \vec{c} \right)$,  if $\vec{a} = 2 \hat {i} + \hat {j} + 3 \hat {k} , \vec{b} = - \hat {i} + 2 \hat {j} + \hat {k}$ and  $\vec{c} = 3 \hat { i} + \hat {j} + 2 \hat {k}$.

#### Solution

The given vectors are $\vec{a} = 2 \hat {i} + \hat {j} + 3 \hat {k} , \vec{b} = - \hat {i} + 2 \hat {j} + \hat {k}$ and $\vec{c} = 3 \hat {i} + \hat {j} + 2 \hat {k}$

Now,

$\vec{b} \times \vec{c} = \begin{vmatrix}\hat { i } & \hat {j} & \hat {k}\\ - 1 & 2 & 1 \\ 3 & 1 & 2\end{vmatrix} = 3\hat { i} + 5 \hat {j} - 7 \hat {k}$

$\therefore \vec{a} . \left( \vec{b} \times \vec{c} \right) = \left( 2 \hat {i} + \hat {j} + 3 \hat {k} \right) . \left( 3 \hat{i} + 5 \hat {j} - 7 \hat {k} \right) = 2 \times 3 + 1 \times 5 + 3 \times \left( - 7 \right) = 6 + 5 - 21 = - 10$

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#### APPEARS IN

RD Sharma Class 12 Maths
Chapter 26 Scalar Triple Product
Very Short Answers | Q 11 | Page 18