Advertisements
Advertisements
प्रश्न
Prove that `[bar"a" bar"b" + bar"c" bar"a" + bar"b" + bar"c"] = 0`
उत्तर
`[bar"a" bar"b" + bar"c" bar"a" + bar"b" + bar"c"]`
`= bar"a" * [(bar"b" + bar"c") xx (bar"a" + bar"b" + bar"c")]`
`= bar"a" * (bar"b" xx bar"a" + bar"b" xx bar"b" + bar"b" xx bar"c" + bar"c" xx bar"a" + bar"c" xx bar"b" + bar"c" xx bar"c")`
`= bar"a" * (bar"b" xx bar"a") + bar"a" * (bar"b" xx bar"b") + bar"a" * (bar"b" xx bar"c") + bar"a" * (bar"c" xx bar"a") + bar"a" * (bar"c" xx bar"b") + bar"a" * (bar"c" xx bar"c")`
`= 0 + 0 + bar"a" * (bar"b" xx bar"c") + 0 - bar"a" * (bar"b" xx bar"c") + 0`
= 0
APPEARS IN
संबंधित 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"]`.
If `bar"c" = 3bar"a" - 2bar"b"`, then prove that `[bar"a" bar"b" bar"c"] = 0`.
Show that `bar"a" xx (bar"b" xx bar"c") + bar"b" xx (bar"c" xx bar"a") + bar"c" xx (bar"a" xx bar"b") = bar"0"`
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"`
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"b" * vec"c")vec"a"`
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"`
`vec"a" = 2hat"i" + 3hat"j" - hat"k", vec"b" = -hat"i" + 2hat"j" - 4hat"k", vec"c" = hat"i" + hat"j" + hat"k"` then find the va;ue of `(vec"a" xx vec"b")*(vec"a" xx 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`
If `vec"a" = hat"i" + 2hat"j" + 3hat"k", vec"b" = 2hat"i" - hat"j" + hat"k", vec"c" = 3hat"i" + 2hat"j" + hat"k"` and `vec"a" xx (vec"b" xx vec"c") = lvec"a" + "m"vec"b" + ""vec"c"`, find the values of l, m, n
`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 a, b, care non-coplanar vectors and p = `("b" xx "c")/(["abc"]), "q" = ("c" xx "a")/(["abc"]), "r" = ("a" xx "b")/(["abc"])`, then a · p + b · q + c · r = ?
Let A(4, 7, 8), B(2, 3, 4) and C(2, 5, 7) be the vertices of a triangle ABC. The length of the internal bisector of angle A is ______
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`
If `overlinec = 3overlinea - 2overlineb` and `[overlinea overlineb + overlinec overlinea + overlineb + overlinec]` = 0 then prove that `[overlinea overlineb overlinec]` = 0
Show that the volume of the parallelopiped whose coterminus edges are `bara barb barc` is `[(bara, barb, barc)].`
If `barc = 3bara - 2barb and [bara barb+barc bara+barb+barc] = 0` then prove that `[bara barb barc] = 0`
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` 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`
