12.2 Position, Unit, & Parallel Vectors

Given that

 $\overrightarrow{OA}=3i+4j-k$  and  $\overrightarrow{OB}=i-4j+2k$  , find  $\overrightarrow{AB}$  

•  $-2i-8j+3k$  

•  $-2i+8k+3k$  

•  $2i-8k-3k$  

•  $2i+8k-3k$  

Answer explanation

Find
 $\overrightarrow{AB}$  

•  $i+4j-5k$  

•  $3i+6j-3k$  

•  $i+4j-3k$  

•  $-i-4j+5k$  

• None of these

Answer explanation

Which of the following is a unit vector in the same direction as

 $6i-3j+2k$  ?

•  $\frac{6}{7}i-\frac{3}{7}j+\frac{2}{7}k$  

•  $42i-21j+14k$  

•  $7i+7j+7k$  

•  $\frac{1}{7}i-\frac{1}{7}j+\frac{1}{7}k$  

• None of these

Answer explanation

Consider the points A(1, -3, 2) and B(-4, 0, 3). Find the distance between A and B. Round to 3 significant figures.

Answer explanation

Which is a vector 2 units long in the direction of

 $i+j+k$  ?

•  $\frac{2}{\sqrt{3}}\left(i+j+k\right)$  

•  $2i+2j+2k$  

•  $\frac{1}{2}\left(i+j+k\right)$  

•  $\sqrt{3}\left(i+j+k\right)$  

Answer explanation

 

Points A and B have coordinates (1, 3, 5) and (3, x, 7). Find all possible values of x if:

 $\left|AB\right|=2\sqrt{3}$  

• 5 and 1

• -5 and -1

• 3 and -2

• -3 and 2

• None of these

Answer explanation

Answer explanation

Given that u and v are parallel, find the value of x.