Find a unit vector perpendicular to the plane `A B C ,` where the coordinates of `A ,B` and C are `A(3,-1,2),B(1,-1,-3)` and `C(4,-3,1)dot`

Find a unit vector perpendicular to the plane ABC, where the coordinates of A,B, and C are A(3,-1,2),B(1,-1,-3) and C(4,-3,1)

A unit vector n perpendicular to the plane determined by the points A (0, -2, 1), B (1, -2, -2) and C (-1, 1, 0)

Find with the help of vectors, the area of the triangle with vertices A(3,-1,2), B(1,-1,-3) and C(4,-3,1)

Find the vector equation of the plane passing through the point A(1, 0, 1), B(1,-1,1) and C (4,-3,2)

Using vectors, find the area of Delta ABC whose vertices are (i) A(1,1,2),B(2,3,5) and C(1,5,5) (ii) A(1,2,3),B(2,-1,4) and C(4,5,-1) (iii) A(3,-1,2),B(1,-1,-3) and C(4,-3,1) (iv) A ( 1,-1,2),B(2,1,-1) and C(3,-1,2).

Let vec a = a_1 hat i + a_2 hat j+ a_3 hat k;vec b = b_1 hat i+ b_2 hat j+ b_3 hat k ; vec c= c_1hat i + c_2 hat j+ c_3 hat k be three non-zero vectors such that vec c is a unit vector perpendicular to both vec a & vec b. If the angle between vec a and vec b is pi/6 , then |(a_1,b_1,c_1),(a_2,b_2,c_2),(a_3,b_3,c_3)|^2=