Vector Addition and Multiplication by Scalars

The video tutorial covers vector operations, including addition, subtraction, and multiplication by scalars. It explains the triangle rule for vector addition, the process of vector subtraction, and the parallelogram law. Examples are provided to illustrate these concepts, and the video concludes with scalar multiplication, highlighting how it affects vector magnitude while preserving direction.

What is the resultant vector when adding vectors a = (2, 3) and b = (5, -4)?

• (7, -1)

• (7, 1)

• (3, -1)

• (3, 1)

When subtracting vector b from vector a, what is the resultant vector if a = (2, 3) and b = (5, -4)?

• (-3, -7)

• (3, -7)

• (3, 7)

• (-3, 7)

In the parallelogram law of vector addition, what does the diagonal of the parallelogram represent?

• The sum of the vectors

• The difference of the vectors

• The average of the vectors

• The product of the vectors

Given vectors AB = 2i + 4j and AC = 6i - j in a parallelogram ABCD, what is the vector AD?

• 4i + 3j

• 4i - 3j

• 8i + 3j

• 8i - 3j

What happens to the direction of a vector when it is multiplied by a scalar?

• It reverses direction

• It becomes perpendicular

• It remains the same

• It changes direction

If vector a = i + 4j is multiplied by 3, what is the new vector?

• 3i + 4j

• i + 4j

• i + 12j

• 3i + 12j

How can you prove that two vectors are parallel using scalar multiplication?

• By showing they have the same magnitude

• By showing they have the same origin

• By showing they have the same direction

• By showing they have the same length