Let → a = ⟨ 2 , 3 ⟩ a → = 〈 2 , 3 〉 and → b = ⟨ 3 , 5 ⟩ b → = 〈 3 , 5 〉 . Find − 3 → a − 3 → b - 3 a → - 3 b →

Answer 1

Note: anytime I do a letter bolded like this, that means it is a vector since Wyzant doesn't have a good system of vector text when it's only a word answer.

a = < 2, 3 >

b = < 3, 5 >

-3a - 3b = ?

Let's take this piece by piece

First, let's triple both vectors so that we get 3a and 3b, we'll be dealing with the negatives momentarily.

3a = < 6, 9 >

3b = < 9, 15 >

Now, you could consider that there is subtraction going on, which is totally valid; it is how the equation is displayed, or, you could factor off the negative of both terms, add them, then multiply by the negative. I will be doing the latter.

3a + 3b = < 6 + 9, 9 + 15 > = < 15, 24 >

-( 3a + 3b ) = -3a - 3b = < -15, -24 >

I hope this helps! Message me in the comments with any questions, comments, or concerns!