Question

Let u = <-5, -9>, v = <6, 8>. Find -8u - 2v.

Answer 1

<28,56>

Explanation:

We have given two vectors and we have to simplify according to given expression.

Given vectors are:

u = <-5,-9> and v = <6,8>

Since, we know that

<a,b> represents vectors ai+bj where i and j are unit vectors along x and y-axis.

Applying above formula on given vectors :

u = -5i-9j and v = 6i+8j

-8u-2v = -8(-5i-9j)-2(6i+8j)

-8u-2v = 40i+72j-12i-16j

Adding like vectors, we have

-8u-2v = (40-12)i+(72-16)j

-8u-2v = 28i + 56j

Hence -8u-2v = <28,56> which is the answer.

Answer 2

The value of -8u-2v is:

28i+56j or in vector form it is: <28,56>

Explanation:

We are given two vectors u and v such that:

u = <-5, -9> and v = <6, 8>.

In vector form it could be represented as:

u=-5i-9j, where i and j represents the unit vector in the direction of x and y axis respectively.

and v=6i+8j

Now we are asked to find the value of:

-8u - 2v.

We know that -8u could be written as:

-8u=-8(-5i-9j)

⇒ -8u=(-8)×(-5)i+(-8)×(-9)j

⇒ -8u=40i+72j

Also -2v is given as:

-2v=-2(6i+8j)

⇒ -2v= (-2)×6i+(-2)×8j

⇒ -2v= -12i-16j

Hence the value of -8u - 2v is:

-8u-2v= 40i+72j-12i-16j

⇒ -8u-2v= 28i+56j

Hence in vector form it could be written as:

<28,56>.