Parallel and Perpendicular Vectors

Identify whether the following vectors are parallel: v = <3, 4>, u = <6, 8>

• (2, 5)

• No

• (1, 2)

• Yes

Identify whether the following vectors are perpendicular: v = <2, -1>, u = <1, 2>

• Maybe

• (3, 4)

• No

• Yes

Find the dot product of the vectors v = <3, 5> and u = <2, -4>

• 3*2 + 5*4 = 6 + 20 = 26

• 3*2 - 5*(-4) = 6 + 20 = 26

• 3*2 - 5*4 = 6 - 20 = -14

• 3*2 + 5*(-4) = 6 - 20 = -14

Determine if two trains traveling at different speeds are parallel

• No

• Maybe

• Not sure

• Yes

Determine if two roads, one going north and the other going east, are perpendicular

• No

• Maybe

• Yes

Solve the problem: Two forces are acting on an object, F1 = <2, 3> N and F2 = <4, 6> N. Determine if they are parallel or perpendicular.

• The forces F1 and F2 are neither parallel nor perpendicular.

• The forces F1 and F2 are anti-parallel.

• The forces F1 and F2 are collinear but not parallel.

• The forces F1 and F2 are parallel.

Identify whether the vectors v = <1, 1> and u = <-1, 1> are parallel

• The vectors v = (1, 1) and u = (-1, 1) are parallel because they have the same direction

• The vectors v = (1, 1) and u = (-1, 1) are parallel because their dot product is zero

• The vectors v = (1, 1) and u = (-1, 1) are not parallel because there is no scalar k such that v = ku.

• The vectors v = (1, 1) and u = (-1, 1) are parallel because they have the same magnitude

Find the dot product of the vectors v = <2, 3> and u = <5, -2>

• The dot product of v and u is: 2*5 + 3*(-2) = 10 - 6 = 4

• The dot product of v and u is: 2*5 + 3*2 = 10 + 6 = 16

• The dot product of v and u is: 2*5 - 3*(-2) = 10 + 6 = 16

• The dot product of v and u is: 2*3 + 5*(-2) = 6 - 10 = -4

Determine if two boats with velocities v = <1, 2> and u = <-2, 1> are moving perpendicular to each other

• Yes

• Not enough information

• Maybe

• No

Determine if the force F = <5, 7> N and the force G = <10, 14> N are parallel

• No, the forces F = (5, 7) N and G = (10, 14) N are not parallel because they have different magnitudes.

• No, the forces F = (5, 7) N and G = (10, 14) N are not parallel because they are in opposite directions.

• No, the forces F = (5, 7) N and G = (10, 14) N are not parallel because their dot product is not zero.

• Yes, the forces F = (5, 7) N and G = (10, 14) N are parallel because G = 2F.