Graphing a vector by applying a negative scalar

The video tutorial explains scalar multiplication of a vector, using vector U as an example. It demonstrates the application of the distributive property to calculate the resultant vector. The tutorial also covers graphing the original and scaled vectors, highlighting the reflection about the origin and the doubling of the vector's length due to the scalar. The explanation includes a discussion on the effects of scaling and reflection.

What mathematical property is applied when multiplying a vector by a scalar?

• Associative Property

• Distributive Property

• Commutative Property

• Identity Property

What is the resultant vector when vector U = (2, -1) is multiplied by -2?

• (-4, -2)

• (-4, 2)

• (2, -4)

• (4, 2)

How does the direction of a vector change when it is multiplied by a negative scalar?

• It reverses direction

• It remains unchanged

• It rotates 90 degrees

• It rotates 180 degrees

What happens to the length of a vector when it is multiplied by a scalar of -2?

• It remains the same

• It doubles

• It halves

• It triples

What geometric transformation occurs when a vector is multiplied by a negative scalar?

• Scaling

• Reflection

• Rotation

• Translation