Question

Suppose we have a two-dimensional vector [u1​,u2​]. Select all the translations that would occur on the vector from the operation [ u1​ , u2​]−[7,−3]. Shift right No horizontal shift No vertical shift Shift down Shift left Shift up

Answer 1

Subtracting [7, -3] from [u1, u2] shifts the vector left by 7 units and up by 3 units due to the reverse directions indicated in vector subtraction.

Step-by-step explanation:

The operation [u1, u2] - [7, -3] on a two-dimensional vector involves subtracting each corresponding component of the second vector from the first. This results in translating the vector in the opposite directions indicated by the second vector. Specifically:

• Since 7 is subtracted from the first component (horizontal), this would shift the vector to the left by 7 units.
• Since -3 is subtracted from the second component (vertical), this equates to adding 3, which results in the vector moving up by 3 units.

Therefore, the translations that occur due to vector subtraction in this example are a shift to the left and a shift upwards.