Find the values of a, so that the following lines are skew: x-1/2 = y-2/3 = z-a/4, x-4/5 = y-1/2 = z.
Answers
here in above question..
z-3/4 will come because x-1/2 & y-2/3 so don't break the series
•Given:-
x-1/2 = y-2/3 = z-a/4, x-4/5 = y-1/2 = z
•To find:-
the values of a
•Solution:-
if, x-1/2 = y-2/3 = z-a/4 = K ....(1)
and
x-4/5 = y-1/2 = z = L ....(2)
From equation (1)
x = 2k + 1...(3)
y = 3k+2 ...(4)
z= 4k+ a ......(5)
From equation (2)
x= 5L + 4....(4)
y= 2L +1 ....(5)
z = L .....(6)
from equation (2) & (5)
we can say that
y= 3k+2 =2L +1
or, (3k+1)/2 = L ....(7)
from equation (7) & (3)
we can write that
4k+a = (3k+1)/2
or,k= (1-a)/5
Now we have to put the value of L in the equation (4)
and
it is
x = 5L +4 = 5×(3k+1)/2 +4
= 15k/2 +5/2+4 ....(8)
From (1) & (8)
2k+1 = 15k/2 +5/2+4
or, -(3+5/2) = 15k/2 - 2k
or, -11/2 = 11k/2
or, k= -1
From equation (1)
x= 2k+1 = 2×(-1) +1 = -1
And now from equation (4)
x= 5L + 4
or, -1 = 5L +4
or, L= -1
and from equation (3)&(6)
-1 = 4k +a
or, -1= 4×(-1) +a
or, a = 3
So the final value of a is 3