AP EAMCET Engineering 21 Sep 2020 Shift 1 Paper

Given vectors u=

∧

i

−2

∧

j

and v=−3

∧

i

+5

∧

j

.
Now, equation of line segment passes through the points u and v is
‌

x−1

4

=‌

y+2

−7

....(i)
Now, the point vectors having position vectors OP=−‌

1

7

∧

i

,OQ=−‌

1

4

∧

j

and OR=−2

∧

i

+3

∧

j

are given.
The point P(−‌

1

7

,0) by putting in line (i)
∵ Point P(−‌

1

7

,0) satisfied the line, so it is on the line segment (i)
The point Q(0,−‌

1

4

) by putting in line (i)
‌

0−1

4

=‌

− 1 4 +2

7

⇒−‌

1

4

=−‌

1

4

∵ Point Q(0,−‌

1

4

) also satisfied the line (i), so it lies on the line segment.
Now, the point R(−2,3), on putting in the equation of line (i) ‌

−2−1

4

≠‌

3+2

−7

∵ Point Q(−2,3) not satisfied the line (i), so it doesn't line on the line segment. Hence, option (a) is correct.