Which of the following vector is orthogonal to [1−13]⎣⎡ 1−13 ⎦⎤ ?
Question
Which of the following vector is orthogonal to [1−13]⎣⎡ 1−13 ⎦⎤ ?
Solution
To find a vector that is orthogonal (perpendicular) to another vector, we need to find a vector that, when dotted with the given vector, gives a result of zero. This is because the dot product of two orthogonal vectors is zero.
The given vector is [1, -1, 3]. Let's say the vector we are looking for is [x, y, z].
So, we need to solve the following equation for x, y, and z:
1x + -1y + 3*z = 0
This equation has infinitely many solutions. One simple solution would be x=1, y=1, z=0. So, the vector [1, 1, 0] is orthogonal to [1, -1, 3].
However, there could be other solutions as well. For example, you could also have x=3, y=3, z=1, giving the vector [3, 3, 1]. This vector is also orthogonal to [1, -1, 3].
So, without more information or constraints, there are infinitely many vectors that could be orthogonal to [1, -1, 3].
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