Advertisements
Advertisements
प्रश्न
Prove that `(bar"a" + 2bar"b" - bar"c"). [(bar"a" - bar"b") xx (bar"a" - bar"b" - bar"c")] = 3 [bar"a" bar"b" bar"c"]`.
उत्तर
`(bar"a" + 2bar"b" - bar"c"). [(bar"a" - bar"b") xx (bar"a" - bar"b" - bar"c")] = 3 [bar"a" bar"b" bar"c"]`
`= (bar"a" + 2bar"b" - bar"c").(bar"a"xxbar"a" - bar"a" xx bar"b" - bar"a" xx bar"c" - bar"b" xx bar"a" + bar"b" xx bar"b" + bar"b" xx bar"c")`
`= (bar"a" + 2bar"b" - bar"c").(bar"0" - bar"a" xx bar"b" - bar"a" xx bar"c" + bar"a" xx bar"b" + bar"0" + bar"b" xx bar"c")`
`= (bar"a" + 2bar"b" - bar"c"). (bar"c" xx bar"a" + bar"b" xx bar"c")`
`= bar"a".(bar"c" xx bar"a") + bar"a".(bar"b"xxbar"c") + 2bar"b".(bar"c" xx bar"a") + 2bar"b".(bar"b"xxbar"c") - bar"c".(bar"c" xx bar"a") - bar"c".(bar"b" xx bar"c")`
`= 0 + bar"a".(bar"b" xx bar"c") + 2bar"b".(bar"c" xx bar"a") + 2 xx 0 - 0 - 0`
`= [bar"a" bar"b" bar"c"] + 2[bar"b" bar"c" bar"a"]`
`= [bar"a" bar"b" bar"c"] + 2[bar"a" bar"b" bar"c"]`
= `3[bar"a" bar"b" bar"c"]`
Notes
The question in the textbook has a printing mistake, it should be `3 [bar"a" bar"b" bar"c"]` not 3 `[bar"a" - bar"b" - bar"c"]`.
APPEARS IN
संबंधित प्रश्न
Prove that `[bar"a" bar"b" + bar"c" bar"a" + bar"b" + bar"c"] = 0`
If `bar"c" = 3bar"a" - 2bar"b"`, then prove that `[bar"a" bar"b" bar"c"] = 0`.
If `bar "a" = hat"i" + 2hat"j" + 3hat"k" , bar"b" = 3hat"i" + 2hat"j"` and `bar"c" = 2hat"i" + hat"j" + 3hat"k"`, then verify that `bar"a" xx (bar"b" xx bar"c") = (bar"a".bar"c")bar"b" - (bar"a".bar"b")bar"c"`
If `bara = hati - 2hatj`, `barb = hati + 2hatj, barc = 2hati + hatj - 2hatk`, then find (i) `bara xx (barb xx barc)` (ii) `(bara xx barb) xx barc`. Are the results same? Justify.
Show that the points A(2, –1, 0) B(–3, 0, 4), C(–1, –1, 4) and D(0, – 5, 2) are non coplanar
If `vec"a" = hat"i" - 2hat"j" + 3hat"k", vec"b" = 2hat"i" + hat"j" - 2hat"k", vec"c" = 3hat"i" + 2hat"j" + hat"k"`, find `(vec"a" xx vec"b") xx vec"c"`
If `vec"a" = hat"i" - 2hat"j" + 3hat"k", vec"b" = 2hat"i" + hat"j" - 2hat"k", vec"c" = 3hat"i" + 2hat"j" + hat"k"`, find `vec"a" xx (vec"b" xx vec"c")`
For any vector `vec"a"`, prove that `hat"i" xx (vec"a" xx hat"i") + hat"j" xx (vec"a" xx hat"j") + hat"k" xx (vec"a" xx hat"k") = 2vec"a"`
Prove that `[vec"a" - vec"b", vec"b" - vec"c", vec"c" - vec"a"]` = 0
If `vec"a" = 2hat"i" + 3hat"j" - hat"k", vec"b" = 3hat"i" + 5hat"j" + 2hat"k", vec"c" = - hat"i" - 2hat"j" + 3hat"k"`, verify that `vec"a" xx (vec"b" xx vec"c") = (vec"a"*vec"c")vec"b" - (vec"a"*vec"b")vec"c"`
If `vec"a", vec"b", vec"c", vec"d"` are coplanar vectors, show that `(vec"a" xx vec"b") xx (vec"c" xx vec"d") = vec0`
`bar"a" xx (bar"b" xx bar"c") + bar"b" xx (bar"c" xx bar"a") + bar"c" xx (bar"a" xx bar"b")` = ?
If `bar"a" = 3hat"i" - 2hat"j" + 7hat"k", bar"b" = 5hat"i" + hat"j" - 2hat"k"` and `bar "c" = hat"i" + hat"j" - hat"k"`, then `[bar"a" bar"b" bar"c"]` = ______.
If `bar"c" = 3bar"a" - 2bar"b"`, then `[bar"a" bar"b" bar"c"]` is equal to ______.
Let `veca = hati + hatj + hatk` and `vecb = hatj - hatk`. If `vecc` is a vector such that `veca.vecc = vecb` and `veca.vecc` = 3, then `veca.(vecb.vecc)` is equal to ______.
`"If" barc=3bara-2barb "and" [bara barb+barc bara+barb+barc]= 0 "then prove that" [bara barb barc]=0 `
If `barc= 3bara - 2barb and [bara barb+barc bara+barb+barc] = "then proved" [bara barb barc] = 0`
Show that the volume of the parallelopiped whose coterminus edges are `bara barb barc` is `[(bara, barb, barc)].`
If `bar"c" = 3bar"a"-2bar"b"` and `[bar"a" bar"b" +bar"c" bar"a" +bar"b" +bar"c"]` = 0 then prove that `[bar"a" bar"b" bar"c"]` = 0
If `barc = 3bara - 2barb and [bara barb+barc bara + barb + barc] = 0` then prove that `[bara barb barc] = 0`
If `barc=3bara-2barb` and `[bara barb+barc bara+barb+barc ]=0` then prove that `[bara barb barc]=0`
If `barc = 3bara - 2barb`, then prove that `[bara barb barc]` = 0.
If, `barc = 3bara - 2barb`, then prove that `[bara barb barc] = 0`
