Question

Find the value of for which the four points with position vectors  -j - k, 4i + 5j + λk, 3i + 9j + 4k and  -4i + 4j + 4k are coplanar.

Answer 1

Formula:-

(iii) Three vectors \(\vec a,\vec b\) and  \(\vec c\) are coplanar if and only if  \(\vec a.(\vec b\times\vec c)=0\)

(iv) if 

Given:-

The four points are coplaner if vector AB, AC, AD are coplanar.

⇒ 4(50 – 25) – 6(15 + 20) + (λ + 1)(15 + 40) = 0.

⇒ λ = 1

Hence the point are coplanar