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Syllabus

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

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.

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

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 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 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.

ABCD is a parallelogram. The position vector of the points A,B and C are respectively, 4i + 5j -10k , 2i-3j+4k and -i+2j+k. Find the vector equation of the line BD. Also reduce it to cartesian form.

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

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

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

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 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)

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

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

cos

^{2 }alpha+ cos^{2 }beeta+cos^{2 }gama+cos^{2 }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^{2}/a^{2}+ y^{2}/b^{2}+ z^{2}/c^{2}= 1 meet the coordinate axes at A, B and C. Find the locus in which centroid of traingle ABC lies.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

cos

^{2}a + cos^{2}b + cos^{2}c + cos^{2}d =4/3Find the foot of the perpendicular from the point P(1,2,3) on the line x-6/3=y-7/2=z-7/-2 ? Also obtain the equation of the plane containing the line and the point (1,2,3).

Kindly provide the solution! Also, please explain how to find the direction ratios when the foot of the perpendicular lies on a line?^{-1}(1/3)what are drs and dcs give example??

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 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

(x-3)/3. = (y+4)/2. = (z-1)/1

and

(x+1)/3. = (y-2)/2. = (z)/1

^{3}. Then find the locus of the centroid of the tetrahedron. Please answer this as quick as possible.Q.1. find the image of the point having position vector i

^{^}+3j^{^}+4k^{^}in the planer

^{-->}. (2i^{^}-j^{^}+ k^{^}) + 3 = 0.1.(-8 , -14)

2.(2, 3)

3.(-2, -3)

4.(13, -5)

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 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

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

how cn we find point of intersection of line and plane ?

line given by : vectr r=2i-j+2k+lambda (3i+4j+2k) and plane given by : vector r.(i-j+k)=5

Find the image of the point

in the plane2i +3j -4kr.(2i-j+k) =3SHOW 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.

^{2}=4ax axis twice the latus rectum prove that the abscissa of this point is twice the ordinatefind 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

^{2}+|a X j|^{2}+|a X k | = 2|a|^{2}find the direction cosines of the lines connected by the relations :l+m+n=0 and 2lm+2ln-mn=0?

(1) 2x+y-3z+6=0

(2) 2x-y+3z-14=0

(3) 2x-y+3z-13=0

(4) None of these

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...

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

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?

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

find the equation of plane containing lines, r= i+j+ lambda(i+2j-k) and r=2i+j+k - mue(-i+j-2k). Find the distance of this plane from the origin and also from the point (2,-2,3).

x+5/1=y+3/4=z-6/-9.Also write down the coordinates of the foot of the perpendicuar from P to the line

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.

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

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.

find the foot of the perpendicular from P(1,2,3) on the line x-6/3 = y-7/2=z-7/-2

find the equation of the plane passing through the line of intersection of the planes

andr. ( i + 3j) -6 =0whose perpendicular distance from origin is unity.r. ( 3i - j - 4k ) =0,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).

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

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