Can you find at least one vector perpendiculr to `3hat(i)-4hat(j)+7hat(k)`?

Answer

`hat(i)+2hat(j)+5/7hat(k)`

Explanation

Let `xhat(i)+yhat(j)+zhat(k)` be perpendicular to `3hat(i)-4hat(j)+7hat(k)`, then their dot product should be zero. So `3x-4y+7z=0`. Take `x=1`,`y=2`, then we get `z=5//7`
So `hat(i)+2hat(j)+5/7 hat(k)` is perpendicular to `3hat(i)-4hat(j)+7hat(k)`
Note: By choosing arbitrarily, the values of x, y and z satisfying the equation `3x-4y+7z=0`, we can get infinite number of vectors perpendicular to `3hat(i)-4hat(j)+7hat(k)`.