Let a and b be real numbers. Find all vectors (2, a, b) orthogonal to (1, - 5, - 4). What are all the vectors that are orthogonal to (1, - 5, - 4) ? Select the correct choice below and, if necessary, fill in any answer boxes within your choice. A. Vectors of the form (2, a, b), where (a, b) = (Type an ordered pair. Use a comma to separate answers as needed.) B. Vectors of the form (2, a,), where a is any real number (Type an expression using a as the variable.) C. There are no vectors of the form (2, a, b), where a and b are real numbers.

Question

Mathematics

Pirate

16 August, 10:32

Let a and b be real numbers. Find all vectors (2, a, b) orthogonal to (1, - 5, - 4). What are all the vectors that are orthogonal to (1, - 5, - 4) ? Select the correct choice below and, if necessary, fill in any answer boxes within your choice. A. Vectors of the form (2, a, b), where (a, b) = (Type an ordered pair. Use a comma to separate answers as needed.) B. Vectors of the form (2, a,), where a is any real number (Type an expression using a as the variable.) C. There are no vectors of the form (2, a, b), where a and b are real numbers.

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Answers (1)

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Jazlynn · Answer 1

B) vector of the form (2, r, (2-5r) / 4)

Step-by-step explanation:

(2, b, c) is orthogonal to (1,-5,-4) if

2*1-5b-4c=0, i. e,

5b+4c=2

We have equation with two variables, so we know that we wil have infinity lot solutions.

Let's b be some real number r, so we have:

4c=2-5r, i. e,

c = (2-5r) / 4.

So there is infinite lot of othogonal vectors of the form: (2, r, (2-5r) / c)) where r is any real number.