# 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:

$a=5 \cdot \ 2 \cdot \ \cos ( (60^\circ \rightarrow rad) = (60 \cdot \ \dfrac{ \pi }{ 180 } \ ) = ) = 5$
$b=5 \cdot \ 2 \cdot \ \cos ( (45^\circ \rightarrow rad) = (45 \cdot \ \dfrac{ \pi }{ 180 } \ ) = ) = 7.071$
$c=5 \cdot \ 2 \cdot \ \cos ( (120^\circ \rightarrow rad) = (120 \cdot \ \dfrac{ \pi }{ 180 } \ ) = ) = -5$

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

Be the first to comment!

#### Following knowledge from mathematics are needed to solve this word math problem:

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 math problems:

1. Triangle
Triangle KLM is given by plane coordinates of vertices: K[11, -10] L[10, 12] M[1, 3]. Calculate its area and itsinterior angles.
2. Three points 2
The three points A(3, 8), B(6, 2) and C(10, 2). The point D is such that the line DA is perpendicular to AB and DC is parallel to AB. Calculate the coordinates of D.
3. Scalar product
Calculate the scalar product of two vectors: (2.5) (-1, -4)
4. Angle between vectors
Find the angle between the given vectors to the nearest tenth of a degree. u = (-22, 11) and v = (16, 20)
5. Cuboids
Two separate cuboids with different orientation in space. Determine the angle between them, knowing the direction cosine matrix for each separate cuboid. u1=(0.62955056, 0.094432584, 0.77119944) u2=(0.14484653, 0.9208101, 0.36211633)
6. 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?
7. Find the 5
Find the equation with center at (1,20) which touches the line 8x+5y-19=0
8. Coordinates of square vertices
The ABCD square has the center S [−3, −2] and the vertex A [1, −3]. Find the coordinates of the other vertices of the square.
9. Square
Points A[-9,7] and B[-4,-5] are adjacent vertices of the square ABCD. Calculate the area of the square ABCD.
The rectangular crossroads comes passenger car and an ambulance, the ambulance left. Passenger car is at 36 km/h and ambulance 47 km/h. Calculate such a relative speed of the ambulance moves to the car.
11. Vector
Calculate length of the vector v⃗ = (9.75, 6.75, -6.5, -3.75, 2).
12. 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?
13. 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.