Question

Among the following, the pair of the vector orthongonal to each other is

• A. [3,4,7], [3,4,7]
• B. [1,0,0], [1,1,0]
• C. [1,0,2], [0,5,0]
• D. [1,1,1], [-1,-1,1]

Answer 1

The correct option is C [1,0,2], [0,5,0]

The two vectors $X_1$ & $X_2$ are said to be orthogonal if $X_1$.$X_2$ = 0

Let $X_1$ = ${\left[\begin{array}{ccc}1& 0& 2\end{array}\right]}^T$ and $X_2$ = ${\left[\begin{array}{ccc}0& 5& 0\end{array}\right]}^T$

So, $X_1,X_2$ = $\left[\begin{array}{c}1\\ 0\\ 2\end{array}\right].\left[\begin{array}{c}0\\ 5\\ 0\end{array}\right]$ = 1x0+0x5+2x0 = 0

Methos II:

For orthogonal vectors : $\overrightarrow{a}.\overrightarrow{b}$ = 0

i.e. if $\overrightarrow{a}$ = $x_{1}i+y_{1}j+z_{1}k$

& $\overrightarrow{b}$ = $x_{2}i+y_{2}j+z_{2}k$

Then: $x_1{x}_2+y_1{y}_2+z_1{z}_2$ = 0

Option 'c' satisfies the condition.