Question

A(2, 3), B(−1, 5), C(−1, 1) and D(−7, 5) are four points in the Cartesian plane, Check if, `bar("CD")` is parallel to `bar("AB")`

Answer 1

Let `bar("a"), bar("b"), bar("c"), bar("d")` be the position vectors of points A, B, C, D respectively.

∴ `bar("a") = 2hat"i" + 3hat"j", bar("b") = -hat"i" + 5hat"j", bar("c") = -hat"i" + hat"j", bar("d") = -7hat"i" + 5hat"j"`

`bar("CD") = bar("d") - bar("c")`

= `(-7hat"i" + 5hat"j") - (-hat"i" + hat"j")`

= `-6hat"i" + 4hat"j"`

= `2(-3hat"i" + 2hat"j")`

`bar("AB") = bar("b") - bar("a")`

= `(-hat"i" + 5hat"j") - (2hat"i" + 3hat"j")`

= `3hat"i" + 2hat"j"`

As `bar("CD") = 2bar("AB"), bar("CD")` and `bar("AB")` are parallel.