If a line  $\frac{x+1}{p} = \frac{y-1}{q} = \frac{z-2}{r}$  where $p=2q=3r$, makes an angle θ with the positive direction of y-axis, then what is cos2θ equal to?

What is the equation of the plane passing through the point (1,1,1) and perpendicular to the line whose direction ratios are (3,2,1)?

A line makes angles α, β and γ with the positive directions of the coordinate axes. If $\$\backslash vec\{a\}=(\backslash sin^2\; \backslash alpha)\backslash hat\{i\}\; +\; (\backslash sin^2\; \backslash beta)\backslash hat\{j\}\; +\; (\backslash sin^2\; \backslash gamma)\backslash hat\{k\}\; \backslash text\{\; and\; \}\; \backslash vec\{b\}\; =\; \backslash hat\{i\}\; +\; \backslash hat\{j\}\; +\; \backslash hat\{k\}\$$ , then what is $\vec{a}.\vec{b}$ equal to?

Consider the following statements with respect to a vector d = (a × b) × c:

I. d is coplanar with a and b.

II. d is perpendicular to c.

Which of the statements given above is/are correct?