Practice Dot Product (2.1) - A vector and its representation - Solid Mechanics

Practice: Dot Product

Lesson 2.1A vector and its representation

Practise this section

9 questions

Flashcard drill
4 cards from this section. Quick, good the night before a test.
Exercise
6 questions · about 4 min · pass mark 70%. Hints available.
Sign up to start the exercise
Quiz
3 questions · about 2 min · pass mark 70%. Hints available.
Sign up to start the quiz

6 sample questions

Question 1.
Calculate the dot product for vectors a = (1, 2) and b = (3, 4).
Show hintHide hint
Use the formula a · b = a1 * b1 + a2 * b2.
Question 2.
What is the dot product of a vector with itself, for example, c = (5, 5)?
Show hintHide hint
Remember, the dot product of a vector with itself yields the square of its magnitude.
3Question 3.
What is the result of the dot product between two perpendicular vectors?
- 1
- 0
- -1
Show hintHide hint
Remember the geometric interpretation.
4Question 4.
True or False: The dot product yields a vector result.
- True
- False
Show hintHide hint
Think about the nature of the output.
Question 5.
Given three vectors: a = (3, 1, 2), b = (1, 4, 0), and c = (2, -1, 3), find the dot product of a and b, and then determine the angle between c and the resultant vector of a and b.
Show hintHide hint
Don't forget to calculate the magnitudes for the final angle determination.
Question 6.
Two vectors have a dot product of -12, Suggest possible values for their magnitudes and the angle between them.
Show hintHide hint
Think about how multiplying positive and negative components give a negative value?

5 more questions in this section. Enroll free to practise them all.