SI Session 2 Vectors

Which one of these does not show an example of Tip to Tail method?

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Time is an example of a

• Vector

• Scalar

Answer explanation

Time is a scalar quantity because it has magnitude but no direction. Scalars are defined by a single value, while vectors have both magnitude and direction. Therefore, the correct answer is Scalar.

A vector is a mathematical structure that has both _______ and _______.

• direction, magnitude

• scope, sequence

• meat, potatoes

• scalar, vector

Answer explanation

A vector is defined as a mathematical entity that possesses both direction and magnitude. This distinguishes it from scalars, which only have magnitude. Therefore, the correct answer is 'direction, magnitude'.

Given an initial point A ( 2, 4 ) and terminal point B ( -8, 7 ), find the component form of the vector AB.

• 〈-10,3〉

• 〈-6,3〉

• 〈10,11〉

• 〈-6,-3〉

Answer explanation

To find vector AB, subtract the coordinates of A from B: B - A = (-8 - 2, 7 - 4) = (-10, 3). Thus, the component form of vector AB is 〈-10, 3〉, which is the correct answer.

Given u = <3, 7> and v =<-5, 4>, find 2v - 3u

• <21, 2>

• <-19, -13>

• <-15, 3>

• 23

Answer explanation

To find 2v - 3u, first calculate 2v = 2<-5, 4> = <-10, 8> and 3u = 3<3, 7> = <9, 21>. Then, subtract: <-10, 8> - <9, 21> = <-19, -13>. Thus, the correct answer is <-19, -13>.

If a boomerang is thrown 20 m in a straight line and returns exactly to the spot it was thrown what is its displacement?

• 20m

• 40m

• 0m

• -20m

Answer explanation

Displacement is the shortest distance from the initial to the final position. Since the boomerang returns to the starting point, the displacement is 0m, despite traveling 20m in total.

If vectors X and Y are added, then the resultant would be best represented by vector _____. 

• A

• B

• C

• D

Answer explanation

When vectors X and Y are added, the resultant vector is represented by vector C, which correctly depicts the combined effect of both vectors in terms of magnitude and direction.

How do you combine vectors if they are in opposite directions?

• Add

• Subtract

• Pythagorean Theorem

• Use trigonometry

Answer explanation

When combining vectors in opposite directions, you subtract their magnitudes. This is because one vector effectively cancels out part of the other, leading to a resultant vector that reflects the difference in their directions.

Which of the following is a vector? (Select all that apply.)

• Acceleration

• Velocity

• Speed

• Displacement

Answer explanation

Acceleration and velocity are vectors because they have both magnitude and direction. Speed and distance are scalar quantities, as they only have magnitude and no direction.

A car drives 30 meters north, then 20 meters west, and finally 40 meters south to reach the gas pump at Bucee’s

What is the correct drawing of vectors?

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