Applications of Vectors: Day 2

Question 1

How do you find the resultant vector in an application question?

Answer 1

1) use cosine law to determine the magnitude of the resultant vector (r^2=a^2+b^2-2(a)(b)cosθ)
2) use sine law to determine the angle and direction of the resultant vector

Question 2

How do you find tension in an application question?

Answer 2

• if the object is @rest or in u.m., EF=0: signifies that the return to the start position in the triangle (0 vectors)*
  1) use sine law TWICE to determine each tension

Question 3

How do you calculate cartesian vectors?

Answer 3

found by moving a vector to start at origin on a cartesian plane, where the endpoint of vector defines the vector
-we use [ , ] to state cartesian vectors

Question 4

What is the magnitude of a vector and how do you calculate it?

Answer 4

the magnitude is found using the Pythagorean theorem (square root of a^2+b^2)
-expressed in mixed radicals form

Question 5

How do you add and subtract cartesian vectors?

Answer 5

• add the x and y components SEPERATELY

- to subtract, add the OPPOSITE

Question 6

How do you multiply cartesian vectors?

Answer 6

use the distrubtive propetry to distrubute the front number to both components within the vector

Question 7

What is a unit vector in x and y directions?

Answer 7

1 unit in x direction = i with vector hat

1 unit in y direction = j with vector hat

Question 8

How do you calculate a unit vector (â)?

Answer 8

find the magnitude of the vector (pyth. theorem.), then put the orginal coordinates over the magnitude
equation: â=1/|a| (a)