Question

Any vector in an arbitrary direction can always be replace by two (or three)
A. parallel vectors which have the original vector as their resultant.
B. mutually perpendicular vectors which have the original vectors as their resultant.
C. arbitrary vectors which have the original vector as their resultant.
D. it is not possible to resolve a vector.

Answer 1

Hint: We can solve this problem with the concept of vector. There are mainly two quantities in the physics, scalar and vector quantities. Scalar quantities have only magnitude for example, mass and electric while vectors are quantities that have magnitude and direction for example like force and weight.

Complete step-by-step answer:
Vector is typically represented as an arrow whose length is proportional to the magnitude and whose direction is the same in the quantity’ direction. Vectors can not be added or subtracted by the simple arithmetic rules because it follows the set of rules for the addition and subtraction. Addition of the vectors is the resultant of all the vectors acting on the body.
Vectors have some property such as: equal vectors have the same magnitude and direction, vectors can be added graphically not arithmetically. A unit vector is the vector which has magnitude 1, we can also call it the direction vector. Equal vectors can be replaced by each other. If we slide a vector parallel to its position it will be the same as before. Any vector in an arbitrary direction can always be replaced by two (or three) arbitrary vectors which have the original vector as their resultant.
Hence the option C is the correct option.

Note: We know that vectors can not be added or subtracted as simple as scalar but by some laws vectors can also go through addition and subtraction. There are laws of triangle and law of parallelogram for addition and subtraction of vectors and cross product and dot product for vector multiplication.