Question

Two vectors 4i+7j and 2i+3j are added. The magnitude of the sum of these vectors is
A) 36 B)100 C)√136 D)136

Answer 1

Answer:option c

Explanation:

Vector sum .

4i + 7j + 2i + 3j

=6i + 10j

.

.magnitude = √6^2 + 10^2

= √36 + 100

=√136

Answer 2

The magnitude of the sum of given vectors will be $\sqrt{136}$. (option C)

Given,

Vectors:

$4i+7j,$

$2i+3j.$

To find,

The magnitude of the sum of these vectors.

Solution,

Firstly, let the given vectors be A and B, as follows.

$\vec A=4i+7j,$

$\vec B=2i+3j.$

Now, when two vectors are given in such a way that,

$\vec A=ai+bj$, and,

$\vec B=pi+qj$

Then, their sum will be given by adding components of i and j separately, as,

$\overrightarrow {A+B}=(a+p)i+(b+q)j$

And, its magnitude will be,

$|A+B|=\sqrt{(a+p)^2+(b+q)^2}$

Thus, for the given vectors,

$\overrightarrow {A+B}=(4i+7j)+(2i+3j)$

$\implies \overrightarrow {A+B} = (4+2)i+(7+3)j$

$\implies \overrightarrow {A+B} = 6i+10j$

So the sum of given vectors A and B is,

$\overrightarrow {A+B} = 6i+10j.$

Now, the magnitude of this sum will be,

$|A+B|=\sqrt{(6)^2+(10)^2} =\sqrt{36+100}$

$\implies | A + B | = \sqrt{136}.$

Therefore, the magnitude of the sum of given vectors will be $\sqrt{136}$. (option C)

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