## Multiplying or dividing vectors by scalars results in a. vectors. b. scalars. c. vectors if multiplied or scalars if divided. d. scalars if

Question

Multiplying or dividing vectors by scalars results in a. vectors. b. scalars. c. vectors if multiplied or scalars if divided. d. scalars if multiplied or vectors if divided.

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1. The correct answer is option A: Vectors

When a vector is multiplied or divided by a scalar, the result is still a vector.

A vector is any quantity that has both magnitude and direction while a scalar is a quantity that can only be described completely by its magnitude without direction.

Hence, when a vector is multiplied or divided by a scalar, the result is still a vector because the operation only acts on the magnitude and not the direction of the vector.

However, a vector can not be divided by another vector .

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2. Let A = i+j+k be a vector and B = 3 be any scalar,
Multiplying A and B,
AB = (i+j+k)3 = 3i+3j+3k

Which is a new vector whose direction is same as the old but it’s 3 times greater in length than the old vector(i+j+k).

Now, dividing A and B,
A/B = (i+j+k)/3 =[tex] frac{1}{3}i + frac{1}{3}j + frac{1}{3}k [/tex]

Which is again a new vector whose direction is same as the old but now it’s 1/3 times small in length than the old vector.

Direction is same because we multiplied by positive scalar. If we multiply A by suppose -1, -4, -1000000 or any negative number, it’s direction will reverse.

Thus, if we multiply a vector with scalar, it’s length increases. If we divide, it shrinks.