Answer:
[tex] \underline{\boxed{\rm \overrightarrow { OD} = 7\hat{i} + 2\hat{j} + 3\hat{k} }}[/tex]
[tex] \rm \overrightarrow{OA} = \hat{i} + \hat{j} + \hat{k}[/tex]
[tex] \rm \overrightarrow{AB} = 3\hat{i} + - 2\hat{j} + \hat{k}[/tex]
[tex] \rm \overrightarrow{BC} = \hat{i} + 2\hat{j} + - 2 \hat{k}[/tex]
[tex] \rm \overrightarrow{CD} = 2\hat{i} + \hat{j} + 3\hat{k}[/tex]
[tex] \rm \overrightarrow{OD } = ?[/tex]
Step-by-step explanation:
We can say that
[tex] \rm \overrightarrow{AB} = \overrightarrow {OB} - \overrightarrow {OA}[/tex]
[tex] \rm \overrightarrow {OB} = \overrightarrow{AB} + \overrightarrow {OA}[/tex]
[tex] \rm \overrightarrow {OB} = (3\hat{i} + - 2\hat{j} + \hat{k}) + (\hat{i} + \hat{j} + \hat{k})[/tex]
[tex] \rm \overrightarrow {OB} = 4\hat{i} + - \hat{j} + 2\hat{k} [/tex]
Again
[tex] \rm \overrightarrow{BC} = \overrightarrow {OC} - \overrightarrow {OB}[/tex]
[tex] \rm \overrightarrow {OC} = \overrightarrow{BC} + \overrightarrow {OB}[/tex]
[tex] \rm \overrightarrow {OC} = ( \hat{i} + 2\hat{j} + - 2 \hat{k} )+ (4\hat{i} + - \hat{j} + 2\hat{k} )[/tex]
[tex] \rm \overrightarrow {OC} = 5\hat{i} + \hat{j} [/tex]
Again,
[tex] \rm \overrightarrow{CD} = \overrightarrow { OD} - \overrightarrow {OC}[/tex]
[tex] \rm \overrightarrow { OD} = \overrightarrow{CD} + \overrightarrow {OC}[/tex]
[tex] \rm \overrightarrow { OD} = (2\hat{i} + \hat{j} + 3\hat{k} ) + ( 5\hat{i} + \hat{j} )[/tex]
[tex] \rm \overrightarrow{OD } = \overrightarrow{OA }+ \overrightarrow{OB} +\overrightarrow{OC }+ \overrightarrow{OD}[/tex]
[tex]\rm \overrightarrow { OD} = (1 + 3 + 1 + 2)\hat{i} + ( 1 - 2 + 2 + 1)\hat{j} +( 1 + 1 - 2 + 3)\hat{k} [/tex]
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Verified answer
Answer:
[tex] \underline{\boxed{\rm \overrightarrow { OD} = 7\hat{i} + 2\hat{j} + 3\hat{k} }}[/tex]
Given:-
[tex] \rm \overrightarrow{OA} = \hat{i} + \hat{j} + \hat{k}[/tex]
[tex] \rm \overrightarrow{AB} = 3\hat{i} + - 2\hat{j} + \hat{k}[/tex]
[tex] \rm \overrightarrow{BC} = \hat{i} + 2\hat{j} + - 2 \hat{k}[/tex]
[tex] \rm \overrightarrow{CD} = 2\hat{i} + \hat{j} + 3\hat{k}[/tex]
To find :
[tex] \rm \overrightarrow{OD } = ?[/tex]
Step-by-step explanation:
We can say that
[tex] \rm \overrightarrow{AB} = \overrightarrow {OB} - \overrightarrow {OA}[/tex]
[tex] \rm \overrightarrow {OB} = \overrightarrow{AB} + \overrightarrow {OA}[/tex]
[tex] \rm \overrightarrow {OB} = (3\hat{i} + - 2\hat{j} + \hat{k}) + (\hat{i} + \hat{j} + \hat{k})[/tex]
[tex] \rm \overrightarrow {OB} = 4\hat{i} + - \hat{j} + 2\hat{k} [/tex]
Again
[tex] \rm \overrightarrow{BC} = \overrightarrow {OC} - \overrightarrow {OB}[/tex]
[tex] \rm \overrightarrow {OC} = \overrightarrow{BC} + \overrightarrow {OB}[/tex]
[tex] \rm \overrightarrow {OC} = ( \hat{i} + 2\hat{j} + - 2 \hat{k} )+ (4\hat{i} + - \hat{j} + 2\hat{k} )[/tex]
[tex] \rm \overrightarrow {OC} = 5\hat{i} + \hat{j} [/tex]
Again,
[tex] \rm \overrightarrow{CD} = \overrightarrow { OD} - \overrightarrow {OC}[/tex]
[tex] \rm \overrightarrow { OD} = \overrightarrow{CD} + \overrightarrow {OC}[/tex]
[tex] \rm \overrightarrow { OD} = (2\hat{i} + \hat{j} + 3\hat{k} ) + ( 5\hat{i} + \hat{j} )[/tex]
[tex] \underline{\boxed{\rm \overrightarrow { OD} = 7\hat{i} + 2\hat{j} + 3\hat{k} }}[/tex]
In Short Technique:-
[tex] \rm \overrightarrow{OD } = \overrightarrow{OA }+ \overrightarrow{OB} +\overrightarrow{OC }+ \overrightarrow{OD}[/tex]
[tex]\rm \overrightarrow { OD} = (1 + 3 + 1 + 2)\hat{i} + ( 1 - 2 + 2 + 1)\hat{j} +( 1 + 1 - 2 + 3)\hat{k} [/tex]
[tex] \underline{\boxed{\rm \overrightarrow { OD} = 7\hat{i} + 2\hat{j} + 3\hat{k} }}[/tex]