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Let v=(7,8) perpendicular to w, what is the vector w?

A) w=(8,−7)

B) w=(−8,7)

C) w=(7,8)

D) w=(−7,−8)

User Sauer
by
9.2k points

1 Answer

4 votes

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).

User Imthepitts
by
8.5k points

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