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### Question Asked by a Student from EXXAMM.com Team

** Q 2272501436. ** The position vectors of the points `P ` and `Q` are

`5 hat(i) + 7 hat(j) -2 hat(k)` and `- 3 hat(i) + 3 hat(j) + 6 hat(k)` respectively. The

vector

`vec(A) = 3 hat(i) - hat(j) +hat(k)` passes through the point `P` and the vector

`vec(B)= -3 hat(i) + 2 hat(j) + 4 hat(k)` passes through the point `Q`. A third

vector `2 hat(i) + 7 hat(j) - 5 hat(k)` intersects vectors `vec(A) ` and `vec(B)`. The

position vectors of the points of intersection are