Maths · Equation of a line; Skew lines, the shortest distance between them and its equation
Find the equation of the plane through the points , \boldsymbol{B}(\mathbf{3}, \
Find the equation of the plane through the points \( \boldsymbol{A}(\mathbf{2}, \mathbf{2}-\mathbf{1}), \boldsymbol{B}(\mathbf{3}, \mathbf{4}, \mathbf{2}) \) and \( \boldsymbol{C}(\boldsymbol{7}, \boldsymbol{0}, \boldsymbol{6}) \)
- A. \( 5 x+2 y-3 z=17 \)
- B. \( 5 x+2 y+3 z=17 \)
- C. \( 5 x+y-3 z=7 \)
- D. \( 5 x+y+3 z=7 \)
Step-by-step solution
Vectors AB = (1,2,3) and AC = (5,-2,7). Normal vector n = AB × AC = (20,8,-12) = 4(5,2,-3). Using point A, plane equation: 5(x-2)+2(y-2)-3(z+1)=0 simplifies to 5x+2y-3z=17.
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