Question

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.

Answer 1

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

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.