1more shortcut which consume means less time
7 Answers
1357find the eqn of line perpendicular to the plane and passing through the given point(suppose A)
Take the image as B on the line you get
get the midpoint of AB....it should lie on the plane
11Another method (highly similar to Manish bhaiya's method):
Drs of normal to the plane are the drs of the lne joining the point to it's img. So find the eqns of the line. Get a general point and subst. it in the eqn of the plane to get point of intersection. Find the point for which this point will be the midpoint for the line segment with object. That will give u the image.
For example:
Find the image of (1,2,4) wrt x+2y+2z=4.
Solution:
Line with drs 1,2,2 passing thro' (1,2,4) has the equations
x-1/1 = y-2/2 = z-4/2 = λ (say)
By equating each to λ, we get a general point on the line to be
Q(λ+1, 2λ+2, 2λ+4)
For this point to lie on the plane,
λ+1+4λ+4+4λ+8 = 4
9λ = -9
So λ=-1
Thus Q is (0, 0, 2)
Thus the image has to be (-1, -2, 0)
HOPE U UNDERSTAND [4]
1i got yaar but short way yaar which consume less time like max. 1min
11dunno for vector form
if the original point is a,b,c
and the image is h,k,l
and equation of plane is lx+my+nz=k
h-a/l=k-b/b=l-c/n=-2(la+mb+nc)/l2+m2+n2
find h,k,l from the above formula
11Rahul, I'm sorry. I don't have a shorter method than this. The only "method" that I know will take lesser time (max. 5s) is "tukka lagana"[3]
If u have any other method, pls suggest it. [1]
1question chhod do sabse asan galat bhi nahi hoga [5][6][9][9]
i don't know other but some long method knows