Vector Operations

Front

What is a vector?

Back

A vector is a quantity that has both magnitude and direction.

Front

What is the resultant vector?

Back

The resultant vector is equal to the sum of two or more vectors.

Front

How do you add two vectors graphically?

Back

To add two vectors graphically, place the tail of the second vector at the head of the first vector and draw the resultant from the tail of the first vector to the head of the second vector.

Front

What is vector subtraction?

Back

Vector subtraction involves finding the difference between two vectors, which can be done by adding the negative of the second vector to the first.

Front

If vector a = (x1, y1) and vector b = (x2, y2), how do you find a + b?

Back

To find a + b, add the corresponding components: (x1 + x2, y1 + y2).

Front

If vector a = (4, -5) and vector b = (-7, 4), what is a - b?

Back

a - b = (4 - (-7), -5 - 4) = (11, -9).

Front

What is the formula for multiplying a vector by a scalar?

Back

If vector a = (x, y) and k is a scalar, then k * a = (k*x, k*y).

Front

If vector a = (5, -7) and vector b = (-12, 2), what is 2b - 4a?

Back

2b - 4a = 2*(-12, 2) - 4*(5, -7) = (-24, 4) - (20, -28) = (-44, 32).

Front

What does it mean for vectors to be equal?

Back

Two vectors are equal if they have the same magnitude and direction.

Front

What is the dot product of two vectors?

Back

The dot product of vectors a = (x1, y1) and b = (x2, y2) is calculated as a · b = x1*x2 + y1*y2.