Let A = (6, -2, 4). Find two vectors C and D which are parallel to A. Are C and D also parallel to each other?
To find vectors parallel to A, we can multiply A by a scalar. Let's choose a scalar of 2:
C = 2A = 2(6, -2, 4) = (12, -4, 8)
Similarly, let's choose a scalar of -3:
D = -3A = -3(6, -2, 4) = (-18, 6, -12)
Both C and D are parallel to A because they are scalar multiples of A. However, C and D are not parallel to each other because they have different directions.
To find two vectors that are parallel to vector A, we can multiply A by any scalar value. Let's choose a scalar value of 2.
C = 2A
= 2(6, -2, 4)
= (12, -4, 8).
D = 2A
= 2(6, -2, 4)
= (12, -4, 8).
Therefore, vectors C and D are both parallel to A. Since they are both scalar multiples of the same vector, they are also parallel to each other.