Question

I need help asap !!!!!!!!

Answer 1

Page 1: 2u - 3v = < -7, 1 >

Page 2: < -7, 9 >

Explanation:

Page 1: Given u and v, we need 2u - 3v. With vectors, you can multiply both terms by any scalar (the coefficient, i.e. 2u, the 2 is the scalar)

2u = 2<1, 2> = <2, 4>

3v = 3<3, 1> = <9, 3>

So 2u - 3v = <2, 4> - <9, 3> = <2 - 9, 4 - 3> = <-7, 1>

Page 2: The same steps apply, but when you see i and j, the coefficient of the i term is the x value, and the coefficient of the j term is the y value, so

3u - 2v = 3< 1, 1> - 2<5, -3> = <3, 3> - <10, -6> = <3 - 10, 3 - (-6)> = <-7, 9>

Answer 2

Answer to Q1:

2u-3v = <-7,1>

Explanation:

We have given two vectors.

u = <1,2> and v = <3,1>

We have to find 2u-3v.

2u-3v = ?

Vectors can be written as

u = i+2j and v = 3i+j

Putting values , we have

2u-3v = 2(i+2j)-3(3i+j)

2u-3v = 2i+4j-9i-3j

Adding like terms, we have

2u-3v = (2-9)i+(4-3)j

2u-3v = -7i+j

2u-3v = <-7,1> which is the answer.

Answer to Q2:

3u-2v = -7i+9j

Explanation:

We have given two vectors.

u = i+j and v = 5i-3j

We have to find 3u-2v.

3u-2v = ?

Putting give values in above equation, we have

3u-2v = 3(i+j)-2(5i-3j)

3u-2v = 3i+3j-10i+6j

Adding like terms , we have

3u-2v = (3-10)i+(3+6)j

3u-2v = -7i+9j which is the answer.