Question

Consider two vectors given by ;

$\quad \qquad \bullet { \tt \overrightarrow{A} = 2 \hat{i} + \hat{k} }$

$\quad \qquad \bullet { \tt \overrightarrow{B} = \hat{j} + 4 \hat{k} }$

Then Find the magnitude of ${ \tt { \overrightarrow{A} + \overrightarrow{B} } }$ ​

Answer 1

Given :

• $\overrightarrow{A} = 2 \hat{ \imath} + \hat{k}$
• $\overrightarrow{B} = \hat{ \jmath} + 4 \hat{k}$

‎ ‎ ‎

To find :

• Magnitude of $\small \overrightarrow{A} + \overrightarrow{B}$

‎ ‎ ‎

Solution :

Magnitude of required sum of vectors is given by,

$\small{:\implies| \overrightarrow{A} + \overrightarrow{B}| =|(2 \hat{ \imath} + \hat{k} ) +( \hat{ \jmath} + 4 \hat{k} )| }$

$\small{:\implies| \overrightarrow{A} + \overrightarrow{B}| =|2 \hat{ \imath} + \hat{k} + \hat{ \jmath} + 4 \hat{k} | }$

$\small{:\implies| \overrightarrow{A} + \overrightarrow{B}| =|2 \hat{ \imath} + \hat{ \jmath} + 5\hat{k} | }$

Now, we know that magnitude of the vector is given by its distance from origin.

Therefore we are applying distance formula,

$\small{:\implies| \overrightarrow{A} + \overrightarrow{B}| = \sqrt{ {2}^{2} + {1}^{2} + {5}^{2} } }$

$\small{:\implies| \overrightarrow{A} + \overrightarrow{B}| = \sqrt{4 + 1 + 25 } }$

$\small{:\implies| \overrightarrow{A} + \overrightarrow{B}| = \sqrt{30 } }$

Hence the magnitude of the required sum of vectors is √30.

Answer 2

Answer

• ${ \tt { Magnitude\:of\:\overrightarrow{A} + \overrightarrow{B} = \sqrt{30}} }$

Calculations

Given

• ${ \tt \overrightarrow{A} = 2 \hat{i} + \hat{k} }$
• ${ \tt \overrightarrow{B} = \hat{j} + 4 \hat{k} }$

To Find

• ${ \tt { Magnitude\:of\:\overrightarrow{A} + \overrightarrow{B} } }$

Solution

$\qquad\qquad\:\:\:{\boxed{\underline{\underline{\tt{\bigstar\:CONCEPT\:\bigstar}}}}}$

Here, we are given two vectors. We have to find out the magnitude of sum of two vectors. Firstly we will find sum of these two vectors, then we can easily found magnitude of sum of two vectors. So, let's do it !!

Finding sum of vectors,

$\tt \longrightarrow\:\overrightarrow{A} + \overrightarrow{B} = (2\hat{i} + \hat{k}) + (\hat{j} + 4 \hat{k})$

$\tt \longrightarrow\:\overrightarrow{A} + \overrightarrow{B} = 2\hat{i} + \hat{k} + \hat{j} + 4 \hat{k}$

$\tt \longrightarrow\:\overrightarrow{A} + \overrightarrow{B} = 2\hat{i} + \hat{j} + 4 \hat{k} + \hat{k}$

$\tt \longrightarrow\:{\underline{\underline{\overrightarrow{A} + \overrightarrow{B} = 2\hat{i} + \hat{j} + 5\hat{k}}}}$

$\boxed{\bf{\pink{\therefore\:Sum\:of\:vectors\:=\:2\hat{i} + \hat{j} + 5\hat{k}}}}$

Now, we have sum of two vectors. So, let's find the magnitude of the sum of two vectors;

Finding magnitude of sum of vectors,

$\tt \longrightarrow\:Magnitude\:of\:\overrightarrow{A} + \overrightarrow{B} = \sqrt{(2)^2 + (1)^2 + (5)^2}$

$\tt \longrightarrow\:Magnitude\:of\:\overrightarrow{A} + \overrightarrow{B} = \sqrt{4 + 1 + 25}$

$\tt \longrightarrow\:Magnitude\:of\:\overrightarrow{A} + \overrightarrow{B} = \sqrt{5 + 25}$

$\tt \longrightarrow\:{\underline{\underline{Magnitude\:of\:\overrightarrow{A} + \overrightarrow{B} = \sqrt{30}}}}$

$\boxed{\bf{\red{\therefore\:Magnitude\:of\:sum\:of\:vectors\:=\:\sqrt{30}}}}$

Know More

Similar Question:

The vectors 5i+ 8j and 2i+ 7j are added. The magnitude of the sum of these vector is

• [a] √274
• [b] 38
• [c] 238
• [d] 560

Answer:

• brainly.in/question/42435326

▬▬▬▬▬▬▬▬▬▬▬▬