Question

If we add two vectors of equal magnitudes but in opposite directions, then we get a
A) Unit vector
B) Unit scalar
C) Zero vector
D) Zero scalar

Answer 1

Hint: While adding two vectors, the X- component will be the sum of X- components of two vectors, Y- component will be the sum of Y- components of two vectors, and Z- component will be the sum of Z- components of the two vectors. And if the direction is opposite then the negative sign will be given to the components.

Complete step by step answer:
Suppose if we have to add or subtract two vectors then the corresponding component in the X direction, Y direction, and Z direction are added or subtracted. The sum of two vectors is often called a resultant vector.
If one vector is $\vec A = ai + bj + ck$ and another one is $\vec B = di + ej + fk$ . when these two vectors are added, then the resultant vector is given as,
$\left( {ai + bj + ck} \right) + \left( {di + ej + fk} \right) = \left( {a + d} \right)i + \left( {b + e} \right)j + \left( {c + f} \right)k$
Given the two vectors are of equal magnitudes but they are in opposite directions. Therefore they will cancel each other. And the resultant vector will be a zero vector.
If one of the vectors is $\vec a = Ai + Bj + Ck$ . And the other one has the same magnitude and is opposite in direction. Therefore, \[\vec b = - Ai - Bj - Ck\]
Then the resultant vector is given as,
$\vec a + \vec b = \left( {A - A} \right)i + \left( {B - B} \right)j + \left( {C - C} \right)k $
$\Rightarrow \vec a + \vec b = 0i + 0j + 0k $

The sum is a zero vector. The answer is option C.

Note:
We have to note that the unit vector means the magnitude of the vector will be unity. And the unit scalar means the one. And the zero scalar means zero itself.