Advertisement Remove all ads

In a parallelogram ABCD, diagonal vectors are bar"AC" = 2hat"i" + 3hat"j" + 4hat"k" and bar"BD" = - 6hat"i" + 7hat"j" - 2hat"k", then find the adjacent side vectors bar"AB" and bar"AD". - Mathematics and Statistics

Advertisement Remove all ads
Advertisement Remove all ads
Sum

In a parallelogram ABCD, diagonal vectors are `bar"AC" = 2hat"i" + 3hat"j" + 4hat"k" and bar"BD" = - 6hat"i" + 7hat"j" - 2hat"k"`, then find the adjacent side vectors `bar"AB" and bar"AD"`.

Advertisement Remove all ads

Solution

ABCD is a parallelogram.

∴ `bar"AB" = bar"DC", bar"AD" = bar"BC"`

`bar"AC" = bar"AB" + bar"BC"`

`= bar"AB" + bar"AD"`     ...(1)

`bar"BD" = bar"BA" + bar"AD" = - bar"AB" + bar"AD"`    ...(2)

Adding (1) and (2), we get

`2bar"AD" = bar"AC" + bar"BD" = (2hat"i" + 3hat"j" + 4hat"k") + (- 6hat"i" + 7hat"j" - 2hat"k")`

`= - 4hat"i" + 10hat"j" + 2hat"k"`

∴ `bar"AD" = 1/2(- 4hat"i" + 10hat"j" + 2hat"k")`

`= - 2hat"i" + 5hat"j" + hat"k"`

From (1), `bar"AB" = bar"AC" - bar"AD"`

`= (2hat"i" + 3hat"j" + 4hat"k") - (- 2hat"i" + 5hat"j" + hat"k")`

`= 4hat"i" - 2hat"j" + 3hat"k"`

Notes

[Note: Answer in the textbook is incorrect.]

Concept: Vectors and Their Types
  Is there an error in this question or solution?
Advertisement Remove all ads

APPEARS IN

Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×