Vector Addition

Front

What is vector addition?

Back

Vector addition is the process of combining two or more vectors to determine a resultant vector. This involves adding the corresponding components of the vectors.

Front

What is a resultant vector?

Back

The resultant vector is the vector that results from the vector addition of two or more vectors. It represents the total effect of the combined vectors.

Front

How do you calculate the magnitude of a vector?

Back

Front

What is the formula for finding the angle of a vector?

Back

Front

If vector A has components A_x = 7 and A_y = 12, what is the magnitude of vector A?

Back

The magnitude of vector A is calculated as follows: @@|A| = ext{sqrt}(7^2 + 12^2) = ext{sqrt}(49 + 144) = ext{sqrt}(193) \\ |A| ext{ is approximately } 13.9.$$

Front

What is displacement?

Back

Displacement is a vector quantity that refers to the change in position of an object. It is the shortest distance from the initial to the final position, along with the direction.

Front

If Bob walks 4 miles west and then 3 miles west, what is his total distance traveled?

Back

Bob's total distance traveled is 4 miles + 3 miles = 7 miles.

Front

What is the difference between distance and displacement?

Back

Distance is a scalar quantity that measures the total path length traveled, while displacement is a vector quantity that measures the shortest straight-line distance from the initial to the final position.

Front

How do you find the resultant of two vectors in the same direction?

Back

To find the resultant of two vectors in the same direction, simply add their magnitudes. For example, if vector A = 5 m and vector B = 3 m, then the resultant R = A + B = 8 m.

Front

How do you find the resultant of two vectors in opposite directions?

Back

To find the resultant of two vectors in opposite directions, subtract the smaller magnitude from the larger one. For example, if vector A = 5 m east and vector B = 3 m west, then the resultant R = A - B = 2 m east.