# Scalar dot product

Calculate u.v if |u| = 5, |v| = 2 and when angle between the vectors u, v is:

a) 60°
b) 45°
c) 120°

Result

a =  5
b =  7.071
c =  -5

#### Solution:

Leave us a comment of example and its solution (i.e. if it is still somewhat unclear...):

Be the first to comment!

#### To solve this example are needed these knowledge from mathematics:

Two vectors given by its magnitudes and by included angle can be added by our vector sum calculator. Most natural application of trigonometry and trigonometric functions is a calculation of the triangles. Common and less common calculations of different types of triangles offers our triangle calculator. Word trigonometry comes from Greek and literally means triangle calculation.

## Next similar examples:

1. Triangle
Triangle KLM is given by plane coordinates of vertices: K[-12, -11] L[-15, -18] M[-13, -12]. Calculate its area and itsinterior angles.
2. Angle between vectors
Find the angle between the given vectors to the nearest tenth of a degree. u = (-22, 11) and v = (16, 20)
3. Find the 10
Find the value of t if 2tx+5y-6=0 and 5x-4y+8=0 are perpendicular, parallel, what angle does each of the lines make with the x-axis, find the angle between the lines?
The rectangular crossroads comes passenger car and an ambulance, the ambulance left. Passenger car is at 43 km/h and ambulance 52 km/h. Calculate such a relative speed of the ambulance moves to the car.
5. Vector
Calculate length of the vector v⃗ = (9.75, 6.75, -6.5, -3.75, 2).
6. Vector sum
The magnitude of the vector u is 12 and the magnitude of the vector v is 8. Angle between vectors is 61°. What is the magnitude of the vector u + v?
7. Three vectors
The three forces whose amplitudes are in ratio 9:10:17 act in the plane at one point so that they are in balance. Determine the angles of the each two forces.
8. Two forces
Two forces with magnitudes of 25 and 30 pounds act on an object at angles of 10° and 100° respectively. Find the direction and magnitude of the resultant force. Round to two decimal places in all intermediate steps and in your final answer.
An airplane leaves an airport and flies due west 120 miles and then 150 miles in the direction S 44.1°W. How far is the plane from the airport (round to the nearest mile)?
A ship travels 84 km on a bearing of 17°, and then travels on a bearing of 107° for 135 km. Find the distance of the end of the trip from the starting point, to the nearest kilometer.
11. Linear independence
Determine if vectors u=(-4; -5) and v=(20; 25) are linear Linear dependent.
12. Vectors
Vector a has coordinates (8; 10) and vector b has coordinates (0; 17). If the vector c = b - a, what is the magnitude of the vector c?
13. Vectors
For vector w is true: w = 2u-5v. Determine coordinates of vector w if u=(3, -1), v=(12, -10)
14. Line
Line p passing through A[-10, 6] and has direction vector v=(3, 2). Is point B[7, 30] on the line p?
15. Unit vector 2D
Determine coordinates of unit vector to vector AB if A[-6; 8], B[-18; 10].
16. 3d vector component
The vector u = (3.9, u3) and the length of the vector u is 12. What is is u3?
17. Vector
Determine coordinates of the vector u=CD if C[19;-7], D[-16,-5].