Given the point, (alpha, - 1, 2), find the value(s) of alpha so the distance fro

Question

Given the point, (alpha, - 1, 2), find the value(s) of alpha so the distance from the point to the plane given by 3x + y + 2z = 6 is 12/squareroot 14. A line is drawn through the point (6, 4, 2) perpendicular to the plane, 2x + z = 12. Find the point(s) on this line that is/are a distance of squareroot 54 units from the point (1, 2, 3). Given the two lines given by y = -3 - t and y = 4 + t^x = 2 - 3t x = 2t _z = 5 + 2t z = 1 - 3t . a.) Find the point at which the lines intersect. b.) Find the angle between the lines. Given the two planes given by 2x - 3y + 4z = 12 and x + 3y - z = 6. a) Show the planes intersect. a.) Find the parametric equations of the line that represents the line of intersection. b.) Find the angle between the planes.

Explanation / Answer

Distance between the point (, -1,2) and the plane 3x+y+2z=6 = (3-1+2*2)/sqrt(3*3+1*1+2*2)=(3+3)/sqrt(14)

This implies that 12=3+3 or =3

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