Common Core: High School - Number and Quantity : Vector Subtraction as the Additive Inverse: CCSS.Math.Content.HSN-VM.B.4c

Study concepts, example questions & explanations for Common Core: High School - Number and Quantity

varsity tutors app store varsity tutors android store

All Common Core: High School - Number and Quantity Resources

6 Diagnostic Tests 49 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #71 : Vector & Matrix Quantities

If \(\displaystyle v=< 10,-10>\), and \(\displaystyle w=< 4,-14>\), what is \(\displaystyle v-w\)?

Possible Answers:

\(\displaystyle < -14,-24>\)

\(\displaystyle < 14,-24>\)

\(\displaystyle < 4,6>\)

\(\displaystyle < 6,4>\)

\(\displaystyle < 14,24>\)

Correct answer:

\(\displaystyle < 6,4>\)

Explanation:

In order to solve this problem, we need to know how to subtract vectors. It is simply subtracting the x components and the y components. 

\(\displaystyle x=(x\: \mbox{component in}\: v) -(x\:\mbox{component in}\: w )\)

\(\displaystyle y=(y\: \mbox{component in}\: v) -(y\:\mbox{component in}\: w )\)

\(\displaystyle (x\: \mbox{component in}\: v)=10\)

\(\displaystyle (x\:\mbox{component in}\: w)=4\)

\(\displaystyle (y\: \mbox{component in}\: v)=-10\)

\(\displaystyle (y\: \mbox{component in}\: w)=-14\)

\(\displaystyle x=10-4=6\)

\(\displaystyle y=-10-(-14)=-10+14=4\)

So our final answer is \(\displaystyle < 6,4>\).

Below is a visual representation.

Screen shot 2016 03 10 at 2.06.50 pm

Example Question #72 : Vector & Matrix Quantities

If \(\displaystyle v=< 2,0>\), and \(\displaystyle w=< 5,-1>\), what is \(\displaystyle v-w\)?

Possible Answers:

\(\displaystyle < 3,1>\)

\(\displaystyle < 1,-3>\)

\(\displaystyle < -3,1>\)

\(\displaystyle < 3,-1>\)

\(\displaystyle < -3,-1>\)

Correct answer:

\(\displaystyle < -3,1>\)

Explanation:

In order to solve this problem, we need to know how to subtract vectors. It is simply subtracting the x components and the y components. 

\(\displaystyle x=(x\: \mbox{component in}\: v) -(x\:\mbox{component in}\: w )\)

\(\displaystyle y=(y\: \mbox{component in}\: v) -(y\:\mbox{component in}\: w )\)

\(\displaystyle (x\: \mbox{component in}\: v)=2\)

\(\displaystyle (x\:\mbox{component in}\: w)=5\)

\(\displaystyle (y\: \mbox{component in}\: v)=0\)

\(\displaystyle (y\: \mbox{component in}\: w)=-1\)

\(\displaystyle x=2-5=-3\)

\(\displaystyle y=0-(-1)=0+1=1\)

So our final answer is \(\displaystyle < -3,1>\).

Below is a visual representation.


Screen shot 2016 03 10 at 2.13.54 pm

All Common Core: High School - Number and Quantity Resources

6 Diagnostic Tests 49 Practice Tests Question of the Day Flashcards Learn by Concept
Learning Tools by Varsity Tutors