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?

The position vectors of three points A, B and C are a, b and c respectively such that $\vec{3a}-\vec{4b}+\vec{c}=\vec{0}$ What is AB:BC equal to?