Question

Let u = <-7, -2>. Find 8u

Answer 1

8u = <-56,-16>

Explanation:

We have given a vector.

u = <-7,-2>

We have to find Multiplication of a constant 8 and a vector u.

8u = ?

A vector <a,b> can be written as ai+bj where i and j are unit vectors along the direction x and y-axis respectively.

Hence, u = -7i-2j

8u = 8(-7i-2j)

Distribute 8 over the parentheses

8u = 8(-7i)+8(-2j)

8u = -56i-16j

We can also write,

8u = <-56,-16> which is the answer.

Answer 2

Hence, the value of 8u is:

-56i-16j.

In vector form it could be represented as:

<-56,-16>

Explanation:

We are given a vector u as:

u=<-7,-2> where -7 represent the x-component and -2 represent the y-component.

Or this vector could also be represented in terms of i and j as:

u= -7i-2j; where i and j represent the unit vectors in the direction of x and y axis respectively.

Now the value of the vector 8u is:

8u=8(-7i-2j)

⇒ 8u=8×(-7)i+8×(-2)j

⇒ 8u=-56i-16j

Hence the value of the vector 8u is:

-56i-16j.

In vector form it could be represented as:

<-56,-16>