Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11

# If → a = 2 → I + 3 → J + 4 → K and → B = 4 → I + 3 → J + 2 → K Find → a × → B . - Physics

If  $\vec{A} = 2 \vec{i} + 3 \vec{j} + 4 \vec{k} \text { and } \vec{B} = 4 \vec{i} + 3 \vec{j} + 2 \vec{k}$ find $\vec{A} \times \vec{B}$.

#### Solution

Given:

$\vec{A} = 2 \hat {i} + 3 \hat {j} + 4 \hat {k}$ and

$\vec{B} = 4 \hat {i} + 3 \hat {j} + 2 \hat {k}$

The vector product of $\vec{A} \times \vec{B}$

can be obtained as follows:

$\vec{A} \times \vec{B} = \begin{vmatrix}\hat {i} & \hat {j} & \hat {k} \\ 2 & 3 & 4 \\ 4 & 3 & 2\end{vmatrix}$

$= \hat {i} \left( 6 - 12 \right) - \hat {j} \left( 4 - 16 \right) + \hat {k} \left( 6 - 12 \right)$

$= - 6 \hat {i} + 12 \hat {j} - 6 \hat {k}$

Concept: What is Physics?
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#### APPEARS IN

HC Verma Class 11, Class 12 Concepts of Physics Vol. 1
Chapter 2 Physics and Mathematics
Exercise | Q 15 | Page 29
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