Final answer:
To find a vector w that is perpendicular to v=(7,8), we must ensure their dot product is zero. The vector w=(8,-7) satisfies this condition, making it the correct answer.
So option (A) is the correct answer.
Step-by-step explanation:
If vector v = (7, 8) is perpendicular to vector w, then their dot product must equal zero. The dot product of two vectors v and w with components (v1, v2) and (w1, w2) is v1 w1 + v2 w2. To find the vector w that is perpendicular to v, we must solve the equation 7w1 + 8w2 = 0 for the components w1 and w2.
Examining the answer choices:
w = (8, -7), then 7*8 + 8*(-7) = 56 - 56 = 0 satisfies our condition for perpendicular vectors.
w = (-8, 7), then 7*(-8) + 8*7 = -56 + 56 ≠ 0, which does not satisfy the condition.
w = (7, 8), then 7*7 + 8*8 = 49 + 64 ≠ 0, which does not satisfy the condition.
w = (-7, -8), then 7*(-7) + 8*(-8) = -49 - 64 ≠ 0, which does not satisfy the condition either.
Therefore, the vector w that is perpendicular to v is (8, -7), which corresponds to answer choice A).