Three Dimensional Geometry Part 2

Given, line ⇒‌

x−1

2

=‌

y+1

3

=‌

z−1

−2

=λ (let)
Any point on this line is B(2λ+1,3λ−1,−2λ+1) and direction ratios of this line =(2,3,−2)=d1
Let given point be A(0,1,2).
Then direction ratio of
AB=(2λ+1,3λ−2,−2λ−1)=d2
∵ Both lines are perpendicular to each other.
∴‌‌d1⋅d2=0
‌2(2λ+1)+3(3λ−2)−2(−2λ−1)=0
⇒‌‌4λ+2+9λ−6+4λ+2=0
⇒‌‌17λ=2
‌λ‌‌λ=2∕17
∴‌ Direction ratio of required line ‌d2=(21,−28,−21)
‌‌=(3,−4,−3)=(−3,4,3)
This line passes through A(0,1,2).
∴ Required equation of line ⇒‌

x−0

−3

=‌

y−1

4

=‌

z−2

3