Show that the found points `A ,B ,C ,D` with position vectors ` vec a , vec b , vec c , vec d` respectively such that 3 ` vec a-2 vec b+5 vec c-6 vec d= vec0` , are coplanar. Also, find the position vector of the point of intersection of the line segments `A C` and `B Ddot`

Explanation

A, B, C, D has position vectors a,b,c,d

`3a−2b+5c−6d=0`

`⇒3a+5c=2b+d`

`⇒3OA+5OC=2OB+6OD`

`⇒(3OA+5OC)/8=(2OB+6OD)/8`
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OQ

​ be the point which divides AC in the ratio `5:3`

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