Question

The arbitrary number $^{\prime}-2^{\prime}$ is multiplied with vector $\vec{A}$ then
(A) The magnitude of vector will be doubled and direction will be same
(B) The magnitude of vector will be doubled and direction will be opposite
(C) The magnitude of vector and its direction remain constant
(D) None of the above

Answer 1

Hint: We should know that vectors are used in science to describe anything that has both a direction and a magnitude. They are usually drawn as pointed arrows, the length of which represents the vector's magnitude. The four major types of vectors are plasmids, viral vectors, cosmids, and artificial chromosomes. Of these, the most commonly used vectors are plasmids. Common to all engineered vectors are an origin of replication, a multicloning site, and a selectable marker. Vectors can be used to represent physical quantities. Most commonly in physics, vectors are used to represent displacement, velocity, and acceleration. Vectors are a combination of magnitude and direction.

 Complete step by step answer When a vector is multiplied by an arbitrary number x, the magnitude of vector changes by x times but the direction remains the same if the vector is multiplied by an arbitrary number x.
The magnitude of the vector changes by x times and the direction reverses due to -ve sign.
So, when arbitrary number -2 is multiplied with vector $\vec{A}$, then the magnitude of the vector will be doubled and direction will be opposite.

 Therefore, the correct answer is Option B.

 Note: We know that triangle law of vector addition states that when two vectors are represented as two sides of the triangle with the order of magnitude and direction, then the third side of the triangle represents the magnitude and direction of the resultant vector. Two vectors are equal if they have the same magnitude and direction. They are parallel if they have the same or opposite direction. We can combine vectors by adding them, the sum of two vectors is called the resultant. One such operation is the addition of vectors. Two vectors can be added together to determine the result (or resultant). For example, a vector directed up and to the right will be added to a vector directed up and to the left.