Question

the magnitude of resultant vector of two vectors given by A=10i+15j and B=5i would be

Answer 1

Answer:

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Answer 2

Answer:

$\sqrt{325}$ , 5 and $15\sqrt{2}$

Explanation:

As given in the question, the two vectors are

$\vec{A}\ =\ 10i\ +\ 15\ j$

and $\vec{B}\ =\ 5i$

Magnitude of vector A is given by,

                            $A\ =\ \sqrt{x^2\ +\ y^2}$

                                 $=\ \sqrt{10^2\ +\ 15^2}$

                                  $=\ \sqrt{100\ +\ 225}$

                                  $=\ \sqrt{325}$

Magnitude of vector B is given by,

                            $B\ =\ \sqrt{x^2\ +\ y^2}$

                                 $=\ \sqrt{5^2\ +\ 0^2}$

                                 $= 5$

Hence, the magnitude of vector A and vector B is $\sqrt{325}$ and 5 respectively.

Now, resultant of vector A and vector B is given by

  $\vec{A}\ +\vec{B}\ =\ 10i\ +\ 15j\ +\ 5i$

                                 $=\ 15i\ +\ 15j$

Magnitude of resultant of vector A and vector B is given by

$A\ +\ B\ =\ \sqrt{x^2\ +\ y^2}$

             $=\ \sqrt{15^2\ +\ 15^2}$

             $=\ \sqrt{450}$

             $=\ 15\sqrt{2}$

Hence, the magnitude of resultant of vector A and vector B is $15\sqrt{2}$