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Vectors and Unit Vector

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The vector A has a magnitude of 3.00 meters. It makes an angle of 30° with respect to the positive x-axis. The vector B has a magnitude of 3.00 meters, but points along the y-axis.

What are the horizontal and vertical components of ?
a) Ax = 2.60, Ay = 1.50
b) Ax = 1.50, Ay = 2.60
c) Ax = 3.00, Ay = 3.00
d) Ax = -2.60, Ay = -1.50

What are the horizontal and vertical components of the?
a) Bx = 0.00, By = 3.00
b) Bx = 3.00, By = 0.00
c) Bx = 3.00, By = 3.00
d) Bx = -2.60, By = -1.50

What is + in unit vector notation?
a) 2.6i + 4.5j
b) 2.6i - 4.5j
c) 6(i + j)
d) 3i + 3j

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Solution Preview

The vector A has a magnitude of 3.00 meters. It makes an angle of 30° with respect to the positive x-axis. The vector B has a magnitude of 3.00 meters, but points along the y-axis.

What are the horizontal ...

Solution Summary

This solution contains step-by-step calculations using trigonometry to determine the horizontal and vertical components of the vector.

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Unit Vectors in Trigonometry

1.) Perform the following operation:
a. v + w = ?
Where, v = 2i - 6j and w = 3i + 4j
b. v - w = ?
Where, v = 8i - 6j and w = - 2i + 4j

2.) Find the dot product of vector v and vector w if:
a. v = 2i - 3j
w = i - j

3.) Find the unit vector that has the same direction as the vector below:
a. v = 4j
b. v = -5j

4.) Perform the following operation for the given equation:
a. -3v for v = -2i - j
b. 5(v) for v = -3i + 2j

5.) a. A vector has the following initial and terminal points respectively:
Initial point: (-1, 1)
Terminal point: (2, -2)
What is the position vector?
b. A vector has the following initial and terminal points respectively:
Initial point: (-1, 2)
Terminal point: (4, 6)
What is the position vector?

6.) Find the magnitude of the following vector:
a. v = 5i + 6j
b. v = -2i - 4j
c. v = 3i - 2j
d. v = 4i - 2j

7.) In what quadrant is the terminal point in the vector below located?
a. v = 5i - 3j

8.) a. The vector, v, is multiplied by a scalar as shown below:
v = -i + j
-3 (v)
In which quadrant will the terminal point of the product vector be?

b. The vector, v, is multiplied by a scalar as shown below:
v = 2i + 2j
-2(v)
In which quadrant will the terminal point of the product vector be?
9.) a. A basketball player shoots a basketball with a speed of 50 feet per second at an angle of 50 degrees upward from the ground. The vector that describes the motion of the basketball is?

b. A football quarterback throws the football, with a speed of 48 feet per second at an angle of 45 degrees upward from the ground. The vector that describes the motion of the football is?

10.) In which quadrant is the terminal point of the vector v = 6i - 10j located?

11.) Find the dot product of vector v and vector w if:
v = -5i + 6j
w = -2i - 3j

12.) In question 12 a vector is described. Express the vector in terms of i and j.
If exact values are not possible, round components to the nearest tenth.
A plane with an airspeed of 450 miles per hour is flying in the direction of N35°W.

13.) The components of v = 240i +300j represent the respective number of gallons of regular and premium gas sold at a gas station. The components of w = 2.90i +3.07j represent the respective prices per gallon for each kind of gas. Find v · w and describe what the answer means in practical terms.

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