Coordinates Of A Point In Space

Given equation of line is

%5Cfrac%7Bx-2%7D%7B1%7D%3D%5Cfrac%7By-1%7D%7B-2%7D%3D%5Cfrac%7Bz-0%7D%7B2%7D%3Dk

[say]
Any point on the line is

Q(k%2B2%2C%5C%2C%5C%2C-2k%2B1%2C2k)

Direction ratios of PQ are

(k%2B2-6%2C-2k%2B1-3%2C2k-9)

ie,

(k-4%2C%5C%2C-2k-2%2C%5C%2C2k-9)%2C

Since, the line

PQ

is perpendicular to

AB

%5Ctherefore

1(k-4)-2(-2k-2)%2B2(2k-9)%3D0

%5CRightarrow

k-4%2B4k%2B4%2B4k-18%3D0

%5CRightarrow

9%5C%2Ck%3D18

%5CRightarrow

k%3D2

%5Ctherefore

Point Q is

(4%2C-3%2C4)

.
Let the image of P about line AB is

R(%7B%7Bx%7D_%7B1%7D%7D%2C%7B%7By%7D_%7B1%7D%7D%2C%7B%7Bz%7D_%7B1%7D%7D)%2C

Where Q is the mid point of PR.

%5Ctherefore

%5Cfrac%7B%7B%7Bx%7D_%7B1%7D%7D%2B6%7D%7B2%7D%3D4%2C%5C%2C%5Cfrac%7B%7B%7By%7D_%7B1%7D%7D%2B3%7D%7B2%7D%3D-3%2C%5C%2C%5Cfrac%7B%7B%7Bz%7D_%7B1%7D%7D%2B9%7D%7B2%7D%3D4

%5CRightarrow

%7B%7Bx%7D_%7B1%7D%7D%3D2%2C%5C%2C%7B%7By%7D_%7B1%7D%7D%3D-9%2C%5C%2C%7B%7Bz%7D_%7B1%7D%7D%3D-1

Chapter Questions
1 MCQs