Vectors

What is the geometric interpretation of the cross product of two vectors?

• The cross product gives a vector that is perpendicular to the plane formed by the two vectors.

• The cross product results in a scalar value representing the area of the parallelogram formed by the vectors.

• The cross product produces a vector that lies in the same plane as the two vectors.

• The cross product indicates the angle between the two vectors.

What is the significance of the zero vector?

• It has a magnitude of 1 and a direction pointing upwards.

• It has a magnitude of 0 and no direction; it is the additive identity in vector addition.

• It is a vector with the maximum possible magnitude.

• It is used to represent a point in space without any direction.

How do you find the component form of a vector given two points R and S?

• Add the coordinates of R and S: RS = R + S.

• Subtract the coordinates of R from S: RS = S - R.

• Multiply the coordinates of R by S: RS = R * S.

• Divide the coordinates of S by R: RS = S / R.

How do you find the angle between two vectors using the dot product?

• Use the formula cos(θ) = (u · v) / (|u| |v|).

• Use the formula sin(θ) = (u × v) / (|u| |v|).

• Use the formula θ = (u · v) + (|u| + |v|).

• Use the formula tan(θ) = (|u| - |v|) / (u · v).

What does it mean for two vectors to be orthogonal?

• Two vectors are orthogonal if their dot product is zero.

• Two vectors are orthogonal if they are of equal length.

• Two vectors are orthogonal if they point in the same direction.

• Two vectors are orthogonal if their magnitudes are equal.

How do you perform vector subtraction?

• Multiply the corresponding components of the vectors.

• Divide the corresponding components of the vectors.

• Subtract the corresponding components of the vectors.

• Add the corresponding components of the vectors.

How do you find a unit vector in the direction of a vector u?

• û = u / |u|

• û = |u| / u

• û = u * |u|

• û = u + |u|

What is the dot product of two vectors u = and v = ?

• u · v = ac + bd

• u · v = a + b + c + d

• u · v = a^2 + b^2 + c^2 + d^2

• u · v = (a + c)(b + d)

If u = <3, 7> and v = <-5, 4>, what is 2v - 3u?

• <-19, -13>

• <-15, -10>

• <-20, -12>

• <-18, -14>

If u = <3, 7>, what is 2u?

• <6, 12>

• <6, 14>

• <3, 14>

• <7, 14>