Algebra - Linear

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

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

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

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

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

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

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

0 2 1 -1

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

-2 2 0 -1

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

The dot products show both pairs are unit vectors Both pairs of vectors are identical 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

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?

0 -v v 1

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

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

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

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

Quiz Questions