Question

If vector A = i +2 j + k, vector B =2i +3k and vector C = 2i +4k , then what is the magnitude of vector A + B -C ?, (I ,j, and k are unit vectors)​

Answer 1

Answer:

i+2j+8k

Explanation:

A+B-C

=i+2j+k+2i+3k-2i+4k

=i+2j+8k

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Answer 2

Explanation:

⇝ Given :-

$\begin{gathered} \vec{ \text A} = \hat\text i + 2 \hat\text j + \hat \text k \\ \end{gathered}$

$\begin{gathered}\vec{\text B} = 2\hat\text i + 3\hat \text k \\ \end{gathered}$

$\begin{gathered}\vec{ \text C} = 2 \hat\text i +4 \hat \text k \\ \end{gathered}$

⇝ To Find :-

$\text{Magnitude of} \: \vec{\text A} + \vec{\text B} - \vec{\text C}$

⇝ Solution :-

★ We Know magnitude of a vector

$\begin{gathered}\vec{\text P}=\text x\hat\text i + \text y \hat\text j+\text z \hat \text k \\\end{gathered}$

★ We Know magnitude of a vector \begin{gathered}\vec{\text P} = \text x\hat\text i + \text y \hat\text j +\text z \hat \text k \\ \end{gathered}[/tex]P =x i^ +y j^ +z k^,

❒ C It is Given by The Formula :

$\begin{gathered}[\tex]</p><p>[tex]\pink{\underbrace{\large\bf|P|= \sqrt{ { x}^{2}+{ y}^{2}+{z}^{2} }} }\\\end{gathered$

Now,

❒ Calculating Value of

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

$begin{gathered}\vec{ \text A} + \vec{\text B}-\vec{\text C}\\\end{gathered$

$\begin{gathered}= \hat\text i+2\hat\text j+\hat \text k + 2\hat\text i+3\hat \text k-(2\hat\text i +4 \hat\text k)\\\end{gathered}$

$\begin{gathered} =3 \hat\text i + 2 \hat{ \text j}+ \cancel{4\hat \text k } - 2\hat\text i - \cancel{4 \hat \text k} \\ \end{gathered}$

$\large= \hat{\text i} + 2 \hat{\text j}$

Hence,

$\large\underline{\pink{\underline{\frak{\pmb{ \vec{ \text{A}} + \vec{B} - \vec{ C} = \hat{i} + 2 \hat{j} }}}}}$

❒ Calculating Magnitude of

$\begin{gathered}[tex]\bf{\vec{A} + \vec{B} - \vec{C}}\\\end{gathered}$

$\begin{gathered}\sf |\vec{A}+\vec{B} -\vec{C}| =\sqrt{ {1}^{2}+{2}^{2} }\\\end{gathered}$

$\begin{gathered}=\sqrt{1 + 4}\\\end{gathered}$

$begin{gathered}=\sqrt{5}\\\end$

Hence,

$\Large\underline{\pink{\underline{\frak{\pmb{|\vec{\text A} + \vec{B} - \vec{C}| = \sqrt{5} }}}}}$