Vector Operations and Properties

What operations are included in vector operations in space?

• Subtraction, division, and magnitude

• Addition, subtraction, and scalar multiplication

• Addition, subtraction, and division

• Multiplication, division, and dot products

How do you add two vectors in three dimensions?

• By dividing each corresponding component

• By adding each corresponding component

• By multiplying each corresponding component

• By subtracting each corresponding component

What is the result of subtracting vector V from vector U?

• The sum of the components of U and V

• The difference of the components of U and V

• The quotient of the components of U and V

• The product of the components of U and V

What is scalar multiplication in the context of vectors?

• Multiplying each component of the vector by a scalar

• Subtracting a scalar from each component of the vector

• Dividing each component of the vector by a scalar

• Adding a scalar to each component of the vector

How is the dot product of two vectors in three dimensions calculated?

• By multiplying the sums of corresponding components

• By subtracting the products of corresponding components

• By dividing the products of corresponding components

• By adding the products of corresponding components

What does the dot product of two vectors result in?

• A scalar

• A matrix

• A vector

• A constant

How is the magnitude of a vector in three dimensions found?

• By dividing the squares of its components

• By subtracting the squares of its components

• By adding the squares of its components

• By multiplying the squares of its components

What is the formula to find the angle between two vectors in three dimensions?

• Sine of theta equals the dot product divided by the sum of magnitudes

• Cosine of theta equals the dot product divided by the product of magnitudes

• Tangent of theta equals the dot product divided by the difference of magnitudes

• Secant of theta equals the dot product divided by the quotient of magnitudes

What is the angle between two vectors if the dot product is positive?

• Obtuse

• Right

• Acute

• Straight

What is the significance of the third coordinate in three-dimensional vector operations?

• It is ignored in calculations

• It is used only in magnitude calculations

• It is only used in scalar multiplication

• It is treated the same as the other two coordinates