Vector Magnitudes
Find the magnitude of the vector <3,4>
5
Find the direction angle of the vector u = <3,2>
33.7 degrees
The term that means the dot product of two vectors is equal to 0.
What is orthogonal (perpendicular)?
Let u= <-1,3> and v= <4,7>, find u+v
<3,10>
A ship is heading due north at 12 mph. The current is flowing southwest at 4 mph. Find the actual bearing and speed of the ship.
342.86 degrees with a speed of 9.6 mph
Find the magnitude of vector 7(cos 135i + sin 135j)
7
What is the direction angle of a vector of 3i - 4j
216.87 degrees
The dot product of <1,1> and <2,3>.
What is 5?
Let u= <-1,3>, v=<2,4>, and w = <2,-5> Find 2u + 3w
<4,-9>
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>
Find the magnitude of the vector PQ where P = (-3,4) and Q = (-5,2)
2√2
Find the direction angle of the vector of 7(cos 135i + sin135j)
135 degrees
The dot product of <3, -1, 6> and <4, -10, 1>.
28
What is the magnitude of ANY unit vector?
1
A ski patroller pulls a toboggan by exerting a constant force of 35 lbs on a handle that makes a 22 degree angle with the horizontal. Determine the work done in pulling the toboggan 200 feet.
6490.3 ft-lb
Find the magnitude of the vector QR where Q = (3,4) and R = (-2,5)
√26
What is the direction angle of the vector <-2,-5>
248.2 degrees
The angle between the vector -3i-2j and 11i-12j. Round the the nearest degree.
What is 99 degrees?
Find the unit vector in the direction of w = -i- 2j
-1/√5i - 2/√5j
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>
Find the magnitude of the vector with initial point (0, -1, 0) and terminal point (1, 2, -2)
√14
Find the direction angle of the vector <3, 4>
53.1 degrees
Find the angle between vector u <-1, 3, 0> and vector v <1, 2, -1>.
49.8 degrees
Find unit vector in component form in the direction of u = <-4,-5>
<-4/√41, -5/√41>
A ship heads due south with the current flowing northwest. Two hours later the ship is 20 miles in the direction 30 degrees west of south from the original starting point. Find the speed with no current of the ship and the rate of the current
13.66 mph