A line has equation rrightarrowt arightarrow t brightarrow

A line has equation r^rightarrow(t) = a^rightarrow + t b^rightarrow where r^rightarrow = x i^rightarrow + y j^rightarrow + z k^rightarrow. a^rightarrow and b^rightarrow are non-zero constant vectors such that a^rightarrow not equaltoo b^rightarrow and a^rightarrow is not perpendicular to b^rightarrow. Which of the equations below represent the plane perpendicular to the line and through the origin. Which of the equations below represent a plane perpendicular to the line and not through the origin. Which of the equations below represent a plane containing the line.

Solution

The line equation has direction ratios of vector b.

Hence plane perpendicular to the line and through the origin will be

(r-0).b =0

So option d (r.b) =0

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If the plane is perpendicular to the line but not through origin is

b.r = ||a||

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c) Plane containing the line will have normal vector equal to axb and also point as a

Hence equation is

axb. (r-a)=0