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Given vectors u=2i-5j and v=6i+kj.

a. Find the value of k to make the two given vectors parallel.
b. Find the value of k to make the two given vectors orthogonal.

User JMat
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1 Answer

2 votes

9514 1404 393

Answer:

  • parallel: -15
  • perpendicular: 2.4

Explanation:

The vectors will be parallel when one is a multiple of the other. That means the ratios of component values are the same:

6/2 = k/-5

k = -5(6/2) = -15

The value of k to make the vectors parallel is -15.

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The vectors will be orthogonal when their dot-product is zero.

(2i -5j) · (6k +kj) = (2)(6) +(-5)(k) = 0

5k = 12 . . . . . . . . add 5k

k = 12/5 = 2.4 . . . . divide by 5

The value of k to make the vectors orthogonal is 2.4.

Given vectors u=2i-5j and v=6i+kj. a. Find the value of k to make the two given vectors-example-1
User Tameek
by
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