When a particle moved from point $A(2,2,3)$ to point $B(6,6,9)$, its displacement vector is

When a particle moved from point $A(2,2,3)$ to point $B(6,6,9)$, its displacement vector is
  1. $4 \hat{\mathbf{i}}+4 \hat{\mathbf{j}}+6 \hat{\mathbf{k}}$
  2. $8 \hat{\mathbf{i}}+8 \hat{\mathbf{j}}+12 \hat{\mathbf{k}}$
  3. $4 \hat{\mathbf{i}}+8 \hat{\mathbf{j}}+6 \hat{\mathbf{k}}$
  4. $8 \hat{\mathbf{i}}+4 \hat{\mathbf{j}}+6 \hat{\mathbf{k}}$

Solution

Given, position $A(2,2,3)$ and position $B(6,6,9)$ Position vector of point $A$ and $B$ $ \begin{aligned} \mathbf{A} & =2 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}+3 \hat{\mathbf{k}} \\ \text { and } \quad \mathbf{B} & =6 \hat{\mathbf{i}}+6 \hat{\mathbf{j}}+9 \hat{\mathbf{k}} \\ \text { Now, } \mathbf{A B} & =\mathbf{B}-\mathbf{A} \\ & =(6-2) \hat{\mathbf{i}}+(6-2) \hat{\mathbf{j}}+(9-3) \hat{\mathbf{k}} \\ & =4 \hat{\mathbf{i}}+4 \hat{\mathbf{j}}+6 \hat{\mathbf{k}} \end{aligned} $

Asked in: AP EAMCET 2021 (23 Aug Shift 1)

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