Question

The dot products of a vector with the vectors (i + j - 3k), (i + 3j - 2k) and (2i + j + 4k) are 0, 5 and 8 respectively. Find the vector.

Answer 1

Let the unknown vector be \(\vec{a}=a\vec{i}+b\vec{j}+c\vec{k}\) 

⇒ 2a + b + 4c = 8 …(3)

Solving equations 1 ,2,3, simultaneously we get:

a = 1,b = 2,c = 1

  \(\vec{a}=\vec{i}+2\vec{j}+\vec{k}\)