TS EAMCET 6-Aug-2021 Shift 1 Question Paper

Line passing through 2

∧

i

+

∧

j

and parallel to

∧

i

+5

∧

j

+2

∧

k

is
‌

x−2

1

=‌

y−1

5

=‌

z

2

=t
Any point taken on the given straight line will be P=(t+2,5t+1,2t)
Let P is the point on the line which is least distance from (3,5,2)=Q (say)
∴ Direction ratios of PQ=⟨t−1,5t−4,2t−2⟩
Now, PQ is perpendicular to the given line.
∴‌‌(t−1)×1+(5t−4)×5+(2t−2)×2=0
⇒‌‌t−1+25t−20+4t−4=0
⇒‌‌30t=25⇒t=25∕30
⇒‌‌t=5∕6
∴‌‌P=(‌

5

6

+2,5×‌

5

6

+1,2×‌

5

6

)=(‌

17

6

,‌

31

6

,‌

10

6

)
∴‌‌PQ‌‌=√(‌

17

6

−3)2+(‌

31

6

−5)2+(‌

10

6

−2)2
‌‌=√(−‌

1

6

)2+(‌

1

6

)2+(−‌

2

6

)2
‌‌=√‌

1+1+4

36

=√‌

6

36

=‌

1

√6