Question

if vector a b is equal to two ICAP - 2 j cap + K cap and o b is equal to 3 ICAP - 4 j cap + 4 k cap find position vector OA
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Answer 1

$\textbf{Given:}$

$\overrightarrow{AB}=\overrightarrow{i}-2\,\overrightarrow{j}+\overrightarrow{k}$

$\overrightarrow{OB}=3\,\overrightarrow{i}-4\,\overrightarrow{j}+4\overrightarrow{k}$

$\textbf{To find:}$

$\overrightarrow{OA}$

$\textbf{Solution:}$

$\textbf{We know that,}$

$\text{Let O be the origin.If A and B are any two points, then}$

$\bf\overrightarrow{AB}=\overrightarrow{OB}-\overrightarrow{OA}$

$\implies\overrightarrow{OA}=\overrightarrow{OB}-\overrightarrow{AB}$

$\implies\overrightarrow{OA}=(3\,\overrightarrow{i}-4\,\overrightarrow{j}+4\overrightarrow{k})-(\overrightarrow{i}-2\,\overrightarrow{j}+\overrightarrow{k})$

$\implies\overrightarrow{OA}=3\,\overrightarrow{i}-4\,\overrightarrow{j}+4\overrightarrow{k}-\overrightarrow{i}+2\,\overrightarrow{j}-\overrightarrow{k}$

$\implies\bf\overrightarrow{OA}=2\,\overrightarrow{i}-2\,\overrightarrow{j}+3\overrightarrow{k}$

$\textbf{Answer:}$

$\bf\overrightarrow{OA}=2\,\overrightarrow{i}-2\,\overrightarrow{j}+3\overrightarrow{k}$

Find more:

If |a| = 13,|b|= 5 and a.b = 60, then

find la xbl.

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