Question

A=3i+4j+5k B=i-j-2k C=2i-3j-3k find |A+B+C|

Answer 1

SOLUTION

GIVEN

$\vec{A} = 3 \hat{i} + 4 \hat{j} + 5 \hat{k}$

$\vec{B} = \hat{i} - \hat{j} - 2 \hat{k}$

$\vec{C} = 2 \hat{i} - 3 \hat{j} - 3 \hat{k}$

TO DETERMINE

$| \vec{A} + \vec{B} + \vec{C} |$

EVALUATION

Here the given three vectors are

$\vec{A} = 3 \hat{i} + 4 \hat{j} + 5 \hat{k}$

$\vec{B} = \hat{i} - \hat{j} - 2 \hat{k}$

$\vec{C} = 2 \hat{i} - 3 \hat{j} - 3 \hat{k}$

Adding three vectors we get

$\vec{A} + \vec{B} + \vec{C}$

$\sf{ =(3 \hat{i} + 4 \hat{j} + 5 \hat{k}) +( \hat{i} - \hat{j} - 2 \hat{k}) + (2 \hat{i} - 3 \hat{j} - 3 \hat{k}) }$

$= 6 \hat{i} + 0 \hat{j} + 0 \hat{k}$

Thus we get

$| \vec{A} + \vec{B} + \vec{C} |$

$= |(6 \hat{i} + 0 \hat{j} + 0 \hat{k})|$

$\sf{ = \sqrt{ {6}^{2} + {0}^{2} + {0}^{2} } }$

$\sf{ = \sqrt{ {6}^{2} } }$

$= 6$

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