Algebra - Linear

Question 1: Can you tell if a dot product of 2 vectors are on the same line?

Only if both vectors have length 1 Yes, but only if the dot product is zero No, the dot product never reveals this Yes, if the dot product equals plus or minus the product of their magnitudes

Question 2: Is there a way to tell the angle between 2 vectors based on the dot product?

Yes, using cos(θ)=(a·b)/(|a||b|) No, dot product gives no angle information Yes, the angle equals the dot product Yes, but only for 2D vectors

Question 3: Is it possible to find the dot product of the vectors [1,2,3] and [1,2,3,4]

Yes, the extra term is dropped No, dot products only work for 2D vectors No, vectors must have the same number of dimensions Yes, the result is 14

Question 4: What is the dot product of the vectors [0,1], and [1,0]?

0 1 -1 2

Question 5: What is the dot product of the vectors [-1,1] and [1,-1]?

-2 -1 2 0

Question 6: What does the result of the vectors in the previous 2 questions mean?

The first pair is perpendicular (dot product 0), and the second pair has an angle greater than 90° (negative dot product) Both pairs of vectors are parallel Both pairs of vectors are identical The dot products show both pairs are unit vectors

Question 7: What is the dot product of the vectors [1,2,3] and [-1,-2,3]?

-4 4 14 -14

Question 8: What is the dot product of the 0 vector, a vector v?

1 -v v 0

Question 9: What is the dot product of the 1 vector, and vector v

The product of the components of v The sum of the components of v v 0

Question 10: What is the dot product of the vector v and vector v

0 2|v| $|v|^2$ 1

Quiz Questions