Understanding Vectors in 3D Space

What is the result of multiplying a vector by a scalar?

• The vector becomes a unit vector

• The vector's length changes

• The vector's direction changes

• The vector's components become zero

How do you calculate the magnitude of a vector?

• Divide each component by the number of components

• Square each component, sum them, and take the square root

• Multiply the components

• Add the components

What is a unit vector?

• A vector with a magnitude of zero

• A vector with a magnitude of one

• A vector with a magnitude greater than one

• A vector with a negative magnitude

What does the hat notation above a vector signify?

• The vector is in 2D space

• The vector is orthogonal

• The vector is a zero vector

• The vector is a unit vector

Which of the following is a standard unit vector in the positive y direction?

• i hat

• l hat

• j hat

• k hat

How can a vector be expressed using standard unit vectors?

• As a division of its components

• As a sum of its components

• As a product of its components

• As a linear combination of i hat, j hat, and k hat

What is the linear combination of the vector (2, -4, 1) using standard unit vectors?

• 2i + 4j + k

• 2i - 4j + k

• 2i + 4j - k

• 2i - 4j - k

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

• Multiply the vector by its magnitude

• Subtract the vector from its magnitude

• Divide the vector by its magnitude

• Add the vector to its magnitude

What is the unit vector in the direction of (3, 12, -4)?

• (3/13, 12/13, -4/13)

• (3, 12, 4)

• (3, 12, -4)

• (13, 12, -4)

What is the magnitude of the vector (4, -2, 1)?

• 21

• Square root of 21

• Square root of 29

• 29