Unit 9 Review Vectors

Finding Magnitude of a Vector

100

Find the magnitude of the vector PQ where p = (-3,4) and Q = (-5,2)

2√2

200

Find the magnitude of the vector PQ where P = (-2,2), and Q = (3,4)

√29

300

Find the magnitude of the vector QR where Q = (3,4) and R = (-2,5)

√26

400

Find the magnitude of the vector <3,4>

5

500

Find the magnitude of vector 7(cos 135i + sin 135j)

7

Finding a Unit Vector

100

find a unit vector in the direction of v= <-3,2>

<-3/√13,2/√13>

200

find unit vector in the direction of u= <-2, 4>

-1/√5i + 2/√5j

300

Find the unit vector in the direction of w = -i- 2j

-1/√5i - 2/√5j

400

Find the unit vector in component form of u = <2,1>

<2/√5, 1/√5>

500

Find unit vector in component form in the direction of u = <-4,-5>

<-4/√41, -5/√41>

Vector operations

100

Let u= <-1,3> and v= <4,7>, find u+v

<3,10>

200

Let u= <-1,3> and v= <4,7>, find 3u

<-3,9>

300

Let u= <-1,3> and v= <4,7>, find 2u+ (-1)v

<-6,-1>

400

Let u= <-1,3>, v=<2,4>, and w = <2,-5> Find 2u + 3w

<4,-9>

500

Let u= <-1,3>, v=<2,4>, and w = <2,-5> Find -2u - 3v

<-4,-18>

Miscellaneous

100

Find the angle between the vectors u and v, given u = 5i-2j and v = i+6j. Round to the nearest whole degree

102 degrees

200

An airplane is flying on a bearing of 335 degrees at 530 mph. Find component form of the velocity of the airplane.

<-223.99, 480.34>

300

An airplane is flying on a bearing of 340 degrees at 325 mph A wind is blowing with the bearing 320 degrees at 40 mph. Find component form of the velocity of the airplane.

<-111.16,305.40>

400

A basketball is shot at a 70 degree angle with the horizontal direction with an initial speed of 10 m/s. Find the component form of the initial velocity.

<3.42,9.40>

500

Find the component form of a vector with a magnitude of 4 in the direction of <3,-8> 

<12/sqrt73, -32/sqrt73>

Finding Direction Angle of a Vector

100

Find the direction angle of the vector u = <3,2>

33.69 degrees

200

What is the direction angle of the vector <-2,-5>

248.2 degrees

300

Find the direction angle of the vector <3, 4>

53.1 degrees

400

What is the direction angle of a vector of 3i - 4j

306.87 degrees

500

Find the direction angle of the vector of 7(cos 135i + sin135j)

135 degrees