Purchase Solution

unit vector

Not what you're looking for?

Ask Custom Question

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.

Attachments
Purchase this Solution

Solution Summary

This solution answers various questions involving unit vectors in trigonometry.

Solution Preview

Dear Student
Please find the attachment for the solutions.

Thank you for using Brainmass

All the best

1.) Perform the following operation:
a. v + w = ?
Where, v = 2i - 6j and w = 3i + 4j
v + w =(2i - 6j)+( 3i + 4j)= 5i -2j
b. v - w = ?
Where, v = 8i - 6j and w = - 2i + 4j
v - w =(8i - 6j)-( -2i + 4j)= 10i -10j
2.) Find the dot product of vector v and vector w if:
a. v = 2i - 3j
w = i - j
v . w =(2i - 3j).( i - j)= 2+3=5
3.) Find the unit vector that has the same direction as the vector below:
a. v = 4j
The required vector is j
b. v = -5j
The required vector is -j
4.) Perform the following operation for the given equation:
a. -3v for v = -2i - j
-3v =-3(-2i - j)= 6i +3j
b. 5(v) for v = -3i + 2j
5(v)= 5(-3i + 2j)= -15i + 10j
5.) a. A vector has the following initial and terminal points ...

Purchase this Solution


Free BrainMass Quizzes
Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

Probability Quiz

Some questions on probability

Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.

Know Your Linear Equations

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

Solving quadratic inequalities

This quiz test you on how well you are familiar with solving quadratic inequalities.