Advertisement Remove all ads

If aijka¯=i^-2j^+3k^ , bijkb¯=4i^-3j^+k^ , cijkc¯=i^-j^+2k^ verify that abcabaca¯×(b¯+c¯)=a¯×b¯+a¯×c¯ - Mathematics and Statistics

Advertisement Remove all ads
Advertisement Remove all ads
Sum

If `bar"a" = hat"i" - 2hat"j" + 3hat"k"`  , `bar"b" = 4hat"i" - 3hat"j" + hat"k"` , `bar"c" = hat"i" - hat"j" + 2hat"k"` verify that `bar"a"xx(bar"b" + bar"c") = bar"a" xx bar"b" + bar"a" xx bar"c"`

Advertisement Remove all ads

Solution

Given: `bar"a" = hat"i" - 2hat"j" + 3hat"k"`  , `bar"b" = 4hat"i" - 3hat"j" + hat"k"` , `bar"c" = hat"i" - hat"j" + 2hat"k"`

∴ `bar"b" + bar"c" = (4hat"i" - 3hat"j" + hat"k") + (hat"i" - hat"j" + 2hat"k")`

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

and `bar"a" xx (bar"b" + bar"c") = |(hat"i",hat"j",hat"k"),(1,-2,3),(4,-3,1)|`

`= (- 6 + 12)hat"i" - (3 - 15)hat"j" + (- 4 +10)hat"k"`

`= 6hat"i" + 12hat"j" + 6hat"k"`    ...(1)

Also, `bar"a" xx bar"b" = |(hat"i",hat"j",hat"k"),(1,-2,3),(4,-3,1)|`

`= (- 2 + 9)hat"i" - (1 - 12)hat"j" + (- 3 + 8)hat"k"`

`= 7hat"i" + 11hat"j" + 5hat"k"`

and `bar"a" xx bar"c" = |(hat"i",hat"j",hat"k"),(1,-2,3),(1,-1,2)|`

`= (- 4+3)hat"i" - (2 - 3)hat"j" + (- 1 + 2)hat"k"`

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

∴ `bar"a" xx bar"b" + bar"a" xx bar"c" = (7hat"i" + 11hat"j" + 5hat"k") + (- hat"i" + hat"j" + hat"k")`

`= 6hat"i" + 12hat"j" + 6hat"k"`     .....(2)

From (1) and (2), we get

`bar"a"xx(bar"b" + bar"c") = bar"a" xx bar"b" + bar"a" xx bar"c"`

Concept: Vector Product of Vectors (Cross)
  Is there an error in this question or solution?
Advertisement Remove all ads
Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×