11.9k views
2 votes
Find a ·
b. |a| = 60, |b| = 30, the angle between a and b is 3π/4.

User Paaacman
by
8.6k points

2 Answers

3 votes

Final answer:

To find the dot product of vectors a and b, we can use the formula: a · b = |a| |b| cos θ, where |a| and |b| are the magnitudes of vectors a and b, and θ is the angle between them.

Step-by-step explanation:

To find the dot product of vectors a and b, we can use the formula: a · b = |a| |b| cos θ, where |a| and |b| are the magnitudes of vectors a and b, and θ is the angle between them.

In this case, |a| = 60 and |b| = 30. The angle between a and b is given as 3π/4.

Therefore, a · b = 60 * 30 * cos (3π/4) = 60 * 30 * (-√2/2) = -1800√2.

User Keimeno
by
8.3k points
0 votes
The dot product is used to determine the magnitude of the resultant vector of two component vectors. It is expressed as a·b. It does not literally mean that you multiply their values. Instead, you multiply their matrices. However, since we cannot find matrices, let's just find the resultant vector through theorems involving triangles. By cosine law:

R = √[a² + b² - 2abcos(3π/4)]
R = √[60² + 30² - 2*60*30*cos(3π/4)]
R = 83.94

Thus, a·b = 83.94
User Thad
by
8.2k points

Related questions

1 answer
2 votes
23.7k views
asked Jun 19, 2019 188k views
Chapmanio asked Jun 19, 2019
by Chapmanio
8.7k points
1 answer
4 votes
188k views
asked Nov 10, 2019 139k views
Stevebot asked Nov 10, 2019
by Stevebot
8.2k points
2 answers
3 votes
139k views