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

Easy.

Correct option is A)

Sum of the vectors

R

=5

i

^

+8

j

^

+2

i

^

+7

j

^

=7

i

^

+15

j

^

magnitude of

R

=∣

R

∣=

49+225

=

274

Answer 2

Answer:

The vectors 5i+ 8j and 2i+ 7jare added. The magnitude of the new vector made as the sum of these vectors is $\sqrt{274}$

Explanation:

• A vector is a physical quantity that has both direction and magnitude to represent it completely

• The addition of two vectors A and B

       $A=a_{1} i+a_{2} j+a_{3} k$  and $B=b_{1} i+b_{2} j+b_{3} k$

       the sum of A and B

      $A + B = (a_{1}+ b_{1}) i+(a_{2}+ b_{2}) j+(a_{3} +b_{3}) k$

• The magnitude of a vector in component form, that is $A=ai+bj+ck$ is given by the formula

        $/A/=\sqrt{a^{2} +b^{2} +c^{2} }$

From the question,

vector A is $A=5i+8j$

vector B is $B=2i+7j$

⇒

$A+B=(5+2)i+(8+7)j=7i+15j$

the magnitude of $/A+B/=\sqrt{7^{2} +15^{2} } =\sqrt{274}$