Intro to Vectors

What is the primary difference between a scalar and a vector quantity?

• A scalar has magnitude, while a vector has only direction.

• A scalar has direction, while a vector has only magnitude.

• A scalar has magnitude only, while a vector has both magnitude and direction.

• A scalar has both magnitude and direction, while a vector has only magnitude.

How are vectors typically denoted?

• By letters in italics.

• By letters in bold font with an arrow on top.

• By letters in bold font only.

• By letters with a line underneath.

If two vectors, one with a magnitude of 4 and another with a magnitude of 3, point in the same direction, what is the magnitude of their resultant vector?

• 1

• 5

• 7

• 12

What mathematical theorem is used to find the magnitude of the resultant vector when adding two perpendicular vectors?

• The Law of Sines

• The Law of Cosines

• The Pythagorean Theorem

• The Quadratic Formula

Are you enjoying the video lesson?

• Yes

• No

How is vector subtraction A - B performed?

• By adding vector A and vector B.

• By adding vector A and the inverse of vector B.

• By subtracting the magnitudes of A and B.

• By reversing the direction of vector A and adding it to B.

What trigonometric function relates the y-component (Ay) of a vector A to its magnitude (A) and the angle (θ) it makes with the x-axis?

• cos θ = Ay / A

• tan θ = Ay / A

• sin θ = Ay / A

• cot θ = Ay / A

When a vector is multiplied by a scalar, what characteristic of the vector changes?

• Only its direction.

• Only its magnitude.

• Both its magnitude and direction.

• Neither its magnitude nor direction.

A boat moves at 4 m/s across a river, and the current pushes it downstream at 1 m/s. What is the magnitude of the boat's resultant velocity?

• 5 m/s

• 3 m/s

• √17 m/s

• √15 m/s