Equality of vectors

In M1, i am very confused with how to make vectors equal. For example in this question; Given that a = 2i + j and b=i+3j find x if a + xb is parallel to the vector i. I know that I have to form some sort of simultaneous equation and the answer is -1/3, but I can't work out how to get there? Thanks!

Reply 1

ValerieKR

10

Original post by mayjb

In M1, i am very confused with how to make vectors equal. For example in this question; Given that a = 2i + j and b=i+3j find x if a + xb is parallel to the vector i. I know that I have to form some sort of simultaneous equation and the answer is -1/3, but I can't work out how to get there? Thanks!

Misread.

Do what RDKGames said

(edited 7 years ago)

Original post by mayjb

In M1, i am very confused with how to make vectors equal. For example in this question; Given that a = 2i + j and b=i+3j find x if a + xb is parallel to the vector i. I know that I have to form some sort of simultaneous equation and the answer is -1/3, but I can't work out how to get there? Thanks!

For the expression to be parallel to i, the j component must be 0.

(edited 7 years ago)

Reply 3

mayjb

OP

1

Original post by RDKGames

For the expression to be parallel to i, the i component must be 0.

I understand that, but I don't know what you do if it gets more complicated and is equal to say -i-3j?? I just don't understand the method you follow to get to the answer.

Original post by mayjb

I understand that, but I don't know what you do if it gets more complicated and is equal to say -i-3j?? I just don't understand the method you follow to get to the answer.

Then yes, simultaneous equations. You would need 2 scalars for both vectors in order to reach any point/vector in the plane from two vectors which aren't parallel to each other, so that's where the two variables come from.

(edited 7 years ago)

Reply 5

B_9710

18

Original post by mayjb

I understand that, but I don't know what you do if it gets more complicated and is equal to say -i-3j?? I just don't understand the method you follow to get to the answer.

Do you understand that if vectors

\mathbf{a}

and

\mathbf{b}

are parallel then

\mathbf{a}=k\mathbf{b}

(scalar constant k), if so it's not too hard to see that a vector parallel to the x axis the vector must be of the form

k\begin{pmatrix} 1 \\ 0 \end{pmatrix}

.

Equality of vectors

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