Question

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.

Answer 1

here in above question..

z-3/4 will come because x-1/2 & y-2/3 so don't break the series

Answer 2

•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