Multiplying or dividing vectors by scalars results in

Asked by maham237 @ 27/04/2021 in Physics viewed by 396 People

a. vectors.
b. scalars.
c. vectors if multiplied or scalars if divided.
d. scalars if multiplied or vectors if divided.

Answered by maham237 @ 27/04/2021

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 = $\frac{1}{3}i + \frac{1}{3}j + \frac{1}{3}k$

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.

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