Question

The vectors 5i+ 8j and 2i+ 7jare added. The magnitude of the sum of these vector is
a) 274
[b] 38
[c] 238
[d] 560​

Answer 1

Correct 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 :

• The magnitude of the sum of these vector is √274.

Explanation :

We are given with the two vectors and we are said the two vectors are added, that is,

• 5i + 8j and 2i + 7j.

We have to find out the magnitude of the sum of these vector.

Given that the two vectors 5i + 8j and 2i + 7j are added.

So, The sum of the two vectors will be,

→ Sum = 5î + 8ĵ + 2î + 7ĵ

→ Sum = 5î + 2î + 8ĵ + 7ĵ

→ Sum = 7î + 8ĵ + 7ĵ

→ Sum = 7î + 15ĵ

Now we have also the value of sum of these two vectors, now we can easily find out the magnitude of the sum of these vectors. So,

→ Magnitude = √(7² + 15²)

→ Magnitude = √(49 + 15²)

→ Magnitude = √(49 + 255)

→ Magnitude = √274

Hence, the magnitude of the sum of these vector is √274. So option (a) is the correct answer for this question.

Answer 2

$\large\underline{\sf{Correct\:Question}}$

$\:$

» 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

$\:$

$\large\underline{\sf{To\:Find}}$

$\:$

» The magnitude of the sum of these vectors?

$\:$

$\large\underline{\sf{Solution}}$

$\:$

$\underbrace{\underline{\sf{\bigstar\:Understanding\:the\:concept\:::}}}$

$\:$

Here, the concept of vectors is used. We are given two vectors i.e, 5i+ 8j and 2i+ 7j, which are added. We have to find out the magnitude of the sum of these vectors? Firslty we will find out the sum to both vectors, After getting their sum we can easily find their magnitude. So, let's solve it!

$\:$

Finding sum of the two vectors,

$\:$

$\sf \longrightarrow\:Sum\:of\:vectors = 5\hat{i} + 8\hat{j} + 2\hat{i} + 7\hat{j}$

$\\ \sf \longrightarrow\:Sum\:of\:vectors = 5\hat{i} + 2\hat{i} + 8\hat{j} + 7\hat{j}$

$\\ \sf \longrightarrow\:\pink{Sum\:of\:vectors = 7\hat{i} + 15\hat{j} }$

$\:$

Now, we have their sum. So, magnitude of their sum ::

$\:$

$\sf \longrightarrow\:Magnitude\:of\:their\:sum = \sqrt{(7)^2 + (15)^2}$

$\\ \sf \longrightarrow\:Magnitude\:of\:their\:sum = \sqrt{49 + 225}$

$\\ \sf \longrightarrow\:\pink{Magnitude\:of\:their\:sum = \sqrt{274}}$

$\:$

$\therefore\:{\underline{\textsf{\textbf{Option\:(a)\:\sf{is\:correct!}}}}}$

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