The vectors $\rm 60 \hat{i}+3 \hat{j}, 40 \hat{i}-8 \hat{j}$ and $\rm \beta \hat{i}-52 \hat{j}$ are collinear if :

Consider the following in respect of the vectors $\rm \vec{a}=(0,1,1)$ and $\rm \vec{b}=(1,0,1) $ :

1. The number of unit vectors perpendicular to both $\rm \vec{a}$ and $\rm \vec{b}$ is only one.

2. The angle between the vectors is $\frac{\pi}{3}$.

Which of the statements given above is/are correct?

If L is the line with direction ratios < 3, -2, 6 > and passing through (1, -1, 1), then what are the coordinates of the points on L whose distance from (1, -1, 1) is 2 units?

Which one of the planes is parallel to the line $\rm \frac{x-2}{3}=\frac{y-3}{4}=\frac{z-4}{5}$ ?