The points , and are vertices of a triangle…

MATHEMATICS · Multi-part · CBSE · Mathematics · Vector Algebra · Vector Algebra

Problem

The points

A(1,2,3)

B(4,-1,2)

and

C(-2,0,5)

are vertices of a triangle

ABC

. (i) Show that the vectors

\overrightarrow{AB}

and

\overrightarrow{AC}

are not parallel. (ii) Find the area of triangle

ABC

. (iii) Obtain a unit vector perpendicular to the plane

ABC

. (iv) Using the result of part (iii), write the vector equation of the line passing through

A

and perpendicular to the plane

ABC