GATE Data Science and Artificial Intelligence 2024 | Sample Paper | Question: 18

Question

Two non-zero vectors $\mathbf{x}$ and $\mathbf{y}$ are perpendicular if 

• A. $\mathbf{x}^{\mathrm{T}} \mathbf{y}=0$
• B. $\mathbf{x}^{\mathrm{T}} \mathbf{y}>0$ 
• C. $\mathbf{x}^{\mathrm{T}} \mathbf{y}<0$
• D. None of the above.

   

Answer 1

Two non-zero vectors \(x\) and \(y\) are perpendicular if their dot product is zero. The dot product of two vectors \(x\) and \(y\) is denoted as \(x^Ty\). Therefore, the condition for \(x\) and \(y\) to be perpendicular is:

\[x^Ty = 0\]

So, the correct option is:

(A) \(x^Ty = 0\)