Question

Explain revolution of vectors.

Determine v1= 3î + 4j +k
v2= î - j - k​

Answer 1

Aиѕωєr —

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Resolution of vectors is the process of splitting up the vectors into two or more vectors so that combines effect of the splitted vectors is same as that of given vector. The vectors in which a given vector is splitted is called component of vector. The components of vector are also vectors. For example , if there are three vectors A , a and b , then A can be expressed as sum of a and b after multiplying them with some real numbers A can be resolved into two components vectors .

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Qυєѕтiσи —

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If $\sf{\vec{v_{1}}=3\hat {i} +4\hat{j}+\hat{k}}$ and $\sf{\vec{v_{2}}=\hat{i}-\hat{j}-\hat{k}}$ , determine the magnitude of $\sf{\vec{v_{1}} + \vec{v_{2}}}$

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Sσℓυтiσи –

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$\qquad\tt{\dashrightarrow \quad \vec{v_{1}}+\vec{v_{2}} = \left(3\hat{i}+4\hat{j}+\hat{k}\right)+\left(\hat{i}-\hat{j}-\hat{k}\right) }$

$\qquad\tt{\dashrightarrow \quad \vec{v_{1}}+\vec{v_{2}} = 3\hat{i}+\hat{i}+4\hat{j}-\hat{j}+\hat{k}-\hat{k}}$

$\qquad\tt{\dashrightarrow \quad \vec{v_{1}}+\vec{v_{2}} = 4\hat{i}+3\hat{j}}$

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Therefore , Magnitude :

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$\qquad\tt{\dashrightarrow \quad \bigg|\vec{v_{1}}+\vec{v_{2}} \bigg|= \sqrt{4^2 + 3^2}}$

$\qquad\tt{\dashrightarrow \quad \bigg|\vec{v_{1}}+\vec{v_{2}} \bigg|= \sqrt{16+9}}$

$\qquad\tt{\dashrightarrow \quad \bigg|\vec{v_{1}}+\vec{v_{2}} \bigg|=\sqrt{25} }$

$\qquad {\pmb{\tt{\dashrightarrow \quad \bigg|\vec{v_{1}}+\vec{v_{2}} \bigg|= 5}}}$

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ㅤㅤㅤㅤ~ Thus, the magnitude of ( v1 + v2 ) is 5 .

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