Vectors Review

Given an initial point R ( -12, 4 ) and terminal point S ( 28, -17 ), find the component form of the vector RS.

• 〈14,-13〉
• 〈-14,13〉
• 〈-40,-21〉
• 〈40,-21〉

Given u = <3, 7> and v =<-5, 4>, find 2v - 3u

• <21, 2>
• <-19, -13>
• <-15, 3>
• 23

Find the dot product if ||v||= 8, ||w||=6 and the angle between them is θ = 240˚

• -24

• 24

• 48

• -48

Find the angle between vectors  $v=-6i–2j$ and  $w=-7i+8j$  

•  $30.38\degree$  

•  $67.25\degree$  

•  $149.62\degree$  

•  $0.53\degree$  

•  $72.91\degree$  

An airplane on course N15W° at 400 mph encounters a wind blowing 35 mph due east.
Find the vector p that represents the plane.

• 400〈cos15i +sin15j〉
• 400〈cos105i +sin105j〉
• 400〈cos75i +sin75j〉
• 15〈cos400i +sin400j〉

Two ships leave port at 4 pm. One is heading at a bearing of N 38^o E and is traveling at 11.5 miles per hour. The other is traveling 13 miles per hour at a bearing of S 47^o E. How far apart are they when dinner is served at 6 pm?

• 18.09 miles

• 36.18 miles

• 80.96 miles

• 48.71 miles

Determine the vector with magnitude 20 in the same direction as <5,-12>.

• <100,-240>

• <-5,12>

• <100/13, -240/13>

• <5/13, -12/13>

A plane that is set to go 500mph wants to go directly East. There is a 40 mph wind heading North. What bearing should the plane head at in order for the resultant to be directly East?

• 94.6 degrees

• 85.4 degrees

• 90 degrees

• 97.2 degrees