Dot Product and Its Applications

What is the result of a dot product between two vectors?

• A scalar

• A matrix

• A tensor

• A vector

If vector A = 2i + 3j + 4k and vector B = 7i + 5j + k, what is their dot product?

• 50

• 40

• 33

• 26

Which formula is used to find the angle between two vectors using the dot product?

• cos(θ) = (A · B) / (|A| + |B|)

• cos(θ) = (A · B) / (|A| * |B|)

• cos(θ) = (A · B) / (|A| - |B|)

• cos(θ) = (A + B) / (|A| * |B|)

What does a dot product of zero between two vectors indicate?

• The vectors are identical

• The vectors are parallel

• The vectors are perpendicular

• The vectors are anti-parallel

Which property of the dot product states that A · B = B · A?

• Transitive

• Commutative

• Distributive

• Associative

What is the dot product of two parallel vectors?

• Equal to the product of their magnitudes

• Equal to the sum of their magnitudes

• Negative of the product of their magnitudes

• Zero

What is the angle between two vectors if their dot product is negative?

• 0 degrees

• 90 degrees

• 180 degrees

• Greater than 90 degrees

If the angle between two vectors is 180 degrees, what is the nature of their dot product?

• Negative

• Undefined

• Zero

• Positive

What happens to the dot product when the angle between two vectors is zero?

• It becomes undefined

• It becomes negative

• It equals the product of their magnitudes

• It becomes zero

Which of the following is NOT a property of the dot product?

• Associative

• Distributive

• Scalar multiplication

• Commutative