Find the perpendicular distance from the point `(1,-3,4)` to the plane – InterviewSolution

InterviewSolution

1.	Find the perpendicular distance from the point `(1,-3,4)` to the plane `3x-4y+12z - 1 = 0`.
Answer» Perpendicular distance from point `(1,-3,4)` to the plane `3x-4y+12z-1 = 0` is `\|(3(1)-4(-3)+12(4)-1)/(sqrt(3^(2)+(-4)^(2)+12^(2)))\|` `= \|(3+12+48-1)/(13)\|=62/13` units.

Discussion

No Comment Found

Related InterviewSolutions

If `alpha,beta ,gamma` are direction angles of a line , then `cos 2alpha + cos 2beta + cos 2 gamma = `A. `-1`B. 0C. 1D. 2
Find the perpendicular distance from the point `(1,-3,4)` to the plane `3x-4y+12z - 1 = 0`.
The direction ratios of vector perpendicular to the two lines whose direction ratios are -2, 1, -1 and -3, -4 , 1 areA. `-3, 5, 11 `B. `3, -5, 11`C. `3, 5, 11 `D. `3, 5, -11`
If direction ratios of two lines are `2,-6,-3 and 4,3,-1` then direction ratios of a line perpendicular to them areA. `2,3,3`B. `3,-2,6`C. `1,2,3`D. `2,-3,6`
Show that the three lines with direction cosines `12/13,-3/13,-4/13,4/13,12/13,3/13,3/13,-4/13,12/13 ` are mutually perpendicular.
If `bar(a),bar(b),bar (c )` are pair wise mutually perpendicular vectors of equal magnitude , then the angle wisv `bar(a)+bar(b)+bar (c )` isA. `cos ^(-1)(1/(sqrt(3)))`B. `cos^(-1)(1/3)`C. `cos^(-1)(2/(sqrt(3)))`D. `cos^(-1)(sqrt(3))`
Find the coordinates of the point where the line through the points A (3, 4, 1) and B(5, 1, 6) crosses the XY-plane.
If a line has direction ratios `2,1,2`.determine its direction cosines.
Direction cosines of the line passing through `A(2,3,-1)and B(-3,-4,2)` areA. `(-5)/(sqrt(83)),(-7)/(sqrt(83)),3/(sqrt(83))`B. `5/(sqrt(83)),7/(sqrt(83)),3/(sqrt(83))`C. `(-7)/(sqrt(83)),3/(sqrt83),(-5)/(sqrt(83))`D. `-5,-7,3`
Two mutually perpendicular straight lines through the origin from an isosceles triangle with the line `2x + y = 5`. Then the area of the triangle is