In (1), if the plane contains the line x=7, (y,z) = (0,1/2) + (3,6)t, it will meet (a) based on the geometry (my line is a perpendicular bisector of the line segment between the two points). Then if it meets (c), it'll automatically meet (b) and (d). So find the plane containing the line and the point.

For (2), you use trig identities to find a relationship between x, y, and z. The identity comes to mind.

For (3), {a,b,c} has a geometrical meaning..., and the dot product being zero has a geometrical meaning....

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