Given vectors u and v, find: 2u + 3v.
u = 〈-1...

Question

Given vectors u and v, find: 2u + 3v.

u = 〈-1, 2〉, v = 〈3, 0〉

Accepted Answer

Hello, everyone. We are asked to consider the vectors A negative 1117 and B 14 0 and determine the following vector seven A plus 12 B. Our answer choices are A, the vector 91 131 B, the vector 91 1 19 C. The vector negative 91 119 D, the vector 245 119. So looking at this, I'm gonna rewrite my seven A plus 12 B and I'm also going to rewrite my vectors. So I know that A is the vector negative 11 17 and B is 14 0. So I'm gonna plug the vector in for the variable. So we will have seven multiplied by the vector negative 1117 and then plus 12 multiplied by the vector 14 0. I'm gonna distribute this in just like I would if these were parentheses. So seven multiplied by negative 11 is negative 77 seven, multiplied by 17 is 119. And then we're gonna add 12, multiplied by 14, which is 168 and 12 multiplied by zero, which is zero. So now I have two vectors that we wanna add together and we're gonna add their corresponding parts together. So we are gonna have a vector and the first value will be negative 77 plus 168 which is 91. And then next would be 119 plus zero, which is 119. So our answer here is the vector 91 119. And that's answer choice B have a nice day.

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Given vectors u and v, find: 2u + 3v.
u = 〈-1, 2〉, v = 〈3, 0〉