3d geometry

Question 1

dist of p from

Answer 1

pa=\/b^2+c^2 y axis\/c^2+a^2

Question 2

centroid

Answer 2

(x1+x2+x3/3 y1+y2+y3/3 z1+z2+z3/3)

Question 3

direction cosine

Answer 3

cos alpha ,cos gamma,cos beta

Question 4

cos

Answer 4

alpha=a/r beta=b/r gamma=c/r

Question 5

cos^2 alpha +cos^2 beta +cos^2gamma

Answer 5

=1 ,l^2+m^2+n^2=1

Question 6

dist b/w two points

Answer 6

\/(x2-x1)^2+(y2-y1)^2+(z2-z1)^2

Question 7

section formula

Answer 7

for internal mx2+nx1/m+n for y change x to y for externally negative

Question 8

ar of triangle

Answer 8

1/2| i j k
| x2-x1 y2-y1 z2-z1
x3-x1 //////////////

Question 9

equation of line in space

Answer 9

x-x1/a=y-y1/b=x-x1/c

Question 10

eq of line passing from 2 points

Answer 10

x-x1/x2-x1 =y-y1/y2-y1=z-z1/z2-z1

Question 11

angle between two intersecting lines

Answer 11

cos@=a1a2+b1b2+c1c2/underroot (a1^2+b1^2+c1^2)(a2^2+b2^2+c2^2)

Question 12

perpendicular line

Answer 12

a1a2+b1b2+c1c2=0

Question 13

angle bw lines in term’s of direction cosines

Answer 13

cos-1(l1l2+m1m2+n1n2)

Question 14

perpendicular line in dc

Answer 14

l1L2+m1m2+n1n2=0

Question 15

coplanar lines

Answer 15

lines which lie in the same plane are called coplanar lines. Any
two coplanar lines are either parallel or intersecting

Question 16

condition for coplanarity of line

Answer 16

for lines x-x1/l1=y-y2/m1=z-z2/n1 and same just change l2 m2 n2 if
x2-x1 y2-y1 z2-z1
l1 m1 n1 =0
l2 m2 n2

Question 17

what is a plane

Answer 17

A plane is a surface such that line joining any two points of
the plane totally lies in it.

Question 18

The general equation of a plane is

Answer 18

a x +by+ cz+ d = 0

Question 19

Plane through the origin is

Answer 19

a x+ by+ cz = 0

Question 20

Planes parallel to coordinate axes

Answer 20

by+ cz +d=0 parallel to X-axis
a x+ cz+ d=0 parallel to Y-axis
a x+ by+ d = 0 parallel to Z-axis

Question 21

If l m, and n are DC’s of normal to the plane, p is the
distance of the origin from the plane, then equation of
plane is

Answer 21

l x + my+ nz = p.

Question 22

Coordinates of foot of perpendicular, drawn from the

origin to the plane, is

Answer 22

(lp mp np ).

Question 23

Plane through a point (x 1y1 z1) is

Answer 23

a(x-x1)+b(y-y1)+z(z-z1)=0

Question 24

Plane ax+by+cz+d=0 intersecting a line segment

joining and divides it in the ratio

Answer 24

ax1+by1+cz1+d/ax2+by2+cz2+d

Question 25

direction ration in terms of points

Answer 25

a=x2-x1 b=y2-y1 c=z2-z1

Question 26

plane parallell to given plane ax+by+cz+d=o is

Answer 26

ax+by+cz+k=0

Question 27

any plane passing through the line of intersection of plane is

Answer 27

(ax+by+cz+d)+k(a1x+b1y+c1z+d1)=0

Question 28

plane through the origin

Answer 28

ax+by+cz=0

Question 29

if a,b,c are intercepts

Answer 29

x/a+y/b+z/c=1

Question 30

when p dist from origin and l m n are direction cosines

Answer 30

lx+my+nz=p

Question 31

vector eqn of plane passing

Answer 31

(r-a).(b x c)=0

Question 32

two plane giving eqn of straight lines

Answer 32

a1x+b1y+c1z+d1=0

a2x+b2y+c2z+d2=0

Question 33

angle between planes

Answer 33

@=cos-1(a1a2+b1b2+c1c2/underoot a1^2+b1^2+c1^2 *underoot a2^2+b2^2+c2^2

Question 34

dist of a pt( x y z) from plane

Answer 34

|ax1+by1+cz1+d | /underoot a^2+b^2c^2

Question 35

distance between two parallel planes

Answer 35

|d1-d2|//underoot a^2+b^2+c^2

Question 36

angle bw a line and a plane

Answer 36

sin@=|a1a2+b1b2+c1c2/underoot a1^2+b1^2+c1^2 *underoot a2^2+b2^2+c2^2

Question 37

projection of line segment

Answer 37

|(x2-x1)L +(y2-y1)M +(z2-z1)n|

Question 38

shortest or distance bw two lines

Answer 38

d=||(c-a) x b|/|b||

Question 39

foot of the perpendicular from a point on the plane ax+by+cz+d=0

Answer 39

eqn=x-x1/a= y-y1/b= z-z1/c

length=a^2+b^2+c^2/underoot a^2+b^2+c^2

Question 40

direction ratio of line joining two points

Answer 40

x2-x1/|pq| same for y and z

Question 41

direction cosine in terms of direction ratios

Answer 41

L=+_ a/underoot a^2+b^2+c^2 for m=b for n=c