Question

Two vectors are equal if and only if?

Answer 1

Vectors are objects that have both magnitudes as well as direction. Similar to scalars which can have positive or negative values, vectors can also be positive or negative. A negative vector can be defined as a vector that points in the direction opposite to the reference positive direction. If two vectors are said to be equal then they should have the same magnitude and direction.

Complete step by step solution:
Two or more vectors are equal when they have the same length, and point in the same direction. The two or more vectors will be equal if they are collinear, codirected, and have the same magnitude. If the two vectors remain equal, their column vectors will also be equal. When the vectors are equal in both their directions must be equal and since it is given in the question that magnitude is the same we can write that option b will be the correct answer for the following question. The other options are not correct for the same reason because the same length vector may have different directions which will render them unequal to each other. The other options are also not correct because even though two vectors may have the same sign and magnitude they can have different positional vectors which will again render them to be unequal to each other.

Note: The vectors are normally associated with the quantities or entities where the direction also becomes important. For example, when we define the velocity of the object we have to also define in which direction the object is traveling so that case we can tell that velocity is a vector quantity, the vectors are extensively used in physics to define both the magnitude attributes and the direction attributes of a given quantity. The direction of the vectors is given by the positional unit vectors in the two-dimensional plane.