find the distance of the point (1,-2,3) from the plane x-y+z=5 measured along a line parellel to x/2=y/3=z/-6

Find distance of the point (-2,3,-4) from the line (x+2)/3=(2y+3)/4=(3z+4)/5, measured parallel to the plane 4x+12y-3z+1=0

find the image of point (1,2,3) in the plane 3x+2y-z=8

 find the image of the point ( 1,6,3) inthe line x/1 = y-1/2 = z-2/3. Also write the equation of the line joining the given point and its image and find the length of the segment joining the given point and its image.

Find the equation of the plane containing the lines--

r = i + j + u(i + 2j - k) and r = i + j + k(-i + j - 2k)

Find the distance of this plane from the origin and also from the point (1,1,1)

Find the distance of the point (a,b,c) from x-axis?

Show that the lines :

(x-1) /2 = (y-2) /3 = (z-3) /4 and (x-4) /5 = (y-1) 2 = z

intersect. find their point of intersection.

If A is a square matrix of order 3 such that |adj A|=225,find |A'|

find the point on the line x+2/3=y+1/2=z-3/2 at a distance 3root2 from the point (1,2,3)

Find the coordinates of the foot of the perpendicular from the point (2,3,-8) to the line (4-x)/2 = y/6 = (1-z)/3. Also find the perpendicular distance from the given point to the given line.

Find the coordinates of the point where the line through (3,-4,-5) and (2,-3,1) crosses the plane 2x + y + z = 7

find the equation of the plane passing through the line of intersection of the planes r. ( i + 3j) -6 =0 and r. ( 3i - j - 4k ) =0, whose perpendicular distance from origin is unity.

find cartesian eqn & vector eqn of the planes passing thru the intersection of the planes r(2i+6j)+12=0 and r(3i-j+4k)=0 which is at unit distance from origin

Q1.  Find the equation of the plane which contains two parallel  lines given by

(x-3) = (y+2) / (-4)= z/5 and (x-4) =(y-3) /(-4) =(z-2) / 5

Find the value of lambda such that the line (x-2)/9 = (y-1)/lambda = (z-3)/6 is perpendicular to the plane 3x - y - 2z = 7

Find the equation of the plane passing through the point P(1,1,1,) and containing the line r=(-3i+j+5k) + A(3i-j-5k). Also show that the plane contains the line r=(-i+2j+5k) + B(i-2j-5k).

Find the distance of the point (3,4,5) from the plane x+y+z= 2 measured parallel to line 2x = y = z.............answer it fast

A line makes angles alpha beeta gama and delta with the diagnols of a cube, prove

cos² alpha+ cos² beeta+cos² gama+cos² delta = 4/3.refer to example number 26th of ncert page 494.is there any easy way of solving this question. i think it is very important from boards point of view. please help

find the distance of the point (1,-2,3) from the plane x-y+z=5 measured parallel to the line x/2=y/3=z/-6.how to solve this type of questions?

cos²a + cos²b + cos²c + cos²d =4/3

Find the equation of the perpendicular drawn from the point (1,-2,3) to the plane 2x - 3y + 4z +9 = 0. Also find the co-ordinates of the

foot of the perpendicular.

Find the length and foot of the perpendicular from the point (1,1,2) to the plane  r.(2i-2j+4k) +5=0?

Sir/Madam

In the problem ,Find the value of lambda Such that the line (X-2)/9 = Y-1/(lambda) = (Z+3)/-6 is perpendicular to the plane

3X-Y-2Z=7. (ans Lambda = - 3)(since line is perpendicular to the plane & parallel to its normal).How do we find the equation of the normal to the given Plane?

find the distance of point (2,3,4) from the plane 3x + 2y + 2z + 5 = 0 measured parallel to the line x+3/3=y-2/6=z/2

find the vector equation of the plane passing through three points with position vectors i + j - 2k, 2i - j + k and i + 2j + k. Also find the coordinates of the point of intersection of the plain and the line r = 3i - j - k + u(2i - 2j + k)

find the equation of the plane whick contains the line of intersection of the planes vector r.(i+2j+3k)-4=0 ,vector r.(2i+j-k)+5=0 and which is perpendicular to the plane vector r.(5i+3j-6k)+8=0.

 Find the equation of the plane passing through the intersection of the planes x-2y+z=1 and 2x+y+z=8 and parallel to th eline with direction ratios proportional to 1,2,1. Find also the perpendicular distance of (1,1,1) from this plane.

Q.1.  find the image of the point having position vector  i^{^} +3j^{^} +4k^{^} in the plane

r^--> . (2i^{^} -j^{^}+ k^{^}) + 3 = 0.

find shortest distance between the line :

x - 8/ 3 = y + 19/ -16 = z - 10/ 7 and x - 15/ 3 = y - 29 /8 = z - 5 / -5

Find the foot of perpendicular drawn from the point A(1, 0, 3) to the joint of the points B(4, 7, 1) and C(3, 5, 3)?

Find the equation of the line passing through the point (-1,3,-2) and perpendicular to the lines x/1 =y/2=z/3 and x+2/5 = y-1/2= z+1/5

show that the lines r=(i+j-k)+ (3i-j) and r= (4i-k)+ u(2i+3k) intersect. also find their point of intersecion.

Show that four points (0,-1,-1) (4,5,1) (3,9,4) (-4,4,4) are coplanar. Also find the equation of the plane containing them.

Show that line whose vector equation is ⃗r= 2i-3j+3k+λ (i-j+4k) is parallel to the plane ⃗r.(i+5j+k)=5 and find the distance between them .

SHOW THAT THE POINTS (0,-1,-1),(4,5,1),(3,9,4) AND (-4,4,4) ARE COPLANAR.ALSO FIND THE EQUATION OF THE LINE CONTAINING THEM.

find the equation of plane passing through the points (3,4,1) and (0,1,0) and parallel to the line (x+3)/2=(y-3)/7=(z-2)/5

A line makes angles alpha ,beta,gamma and delta with diagonals of ther cube,prove that - cos ^ 2 alpha + cos ^ 2 beta + cos ^ 2 gamma + cos ^ 2 delta = 4 / 3

find the equation of line passing through the point (1,-1,1) and perpendicular to the lines joining the points (4,3,2), (1,-1,0) and (1,2,-1), (2,1,1)

find the direction cosines of the lines connected by the relations :l+m+n=0 and 2lm+2ln-mn=0?

Find the vector equation of the plane passing through the points (3, 4, 2) and (7, 0, 6) and

perpendicular to the plane 2x - 5y - 15 = 0. Also show that the plane thus obtained contains

®
the line r = i + 3j - 2k + l (i - j + k).

what is the difference between direction cosines and direction ratios??

What is the cosine of the angle which the vector √2 i + j + k makes with y-axis

Find equation of plane passing through the point (-1,3,2) and perpendicular to each of the planes x+2y+3z=5 and 3x+3y+z=0.

Find the image of the point (2, -1, -5) in the line (x-11)/10 = (y+2)/-4 = (z+8)/-11. Also find the equation of the line joining the given point and its image. Find the length of that line-segment also.

find the equation of the line passing through the point P(4,6,2) and the point of the intersection of the line x-1/3=y/2=z+1/7 and the plane x+y-z=8. Plz help me out with this question...

Find the coordinates of the point where the line through (5, 1, 6) and

(3, 4, 1) crosses the YZ-plane

 The cartisian equation of a line arc 6x-2=3y+1=2z-2.Find 
a)The direction ratio of the line ?

b)Cartisian and vector equations of the line parallel to this line and passing through the point      (2,-1,-1).

From the point P(1,2,4) ,a perpendicular is drawn on the plane 2x+y-2z+3=0. Find the eqn , the length and the coordinate of the foot of perpendicular.

ho we can proof that two lines are coplanar?

How to find the image of the point (3, -2, 1) in the plane 3x - y + 4z = 2.

What is the equation of the planes containing two lines???