Advertisements
Advertisements
प्रश्न
Prove that `[vec"a" - vec"b", vec"b" - vec"c", vec"c" - vec"a"]` = 0
Advertisements
उत्तर
`[vec"a" - vec"b", vec"b" - vec"c", vec"c" - vec"a"] = (vec"a" - vec"b")*[(vec"b" - vec"c") xx (vec"c" - vec"a")]`
= `(vec"a" - vec"b")*[vec"b" xx vec"c" - vec"b" xx vec"a" - vec"c" xx vec"c" + vec"c" xx vec"a"]`
= `vec"a"*(vec"b" xx vec"c") - vec"a"*(vec"b" xx vec"a") - vec"a"*(vec"c" xx vec"c") + vec"a"*(vec"c" xx vec"a") - vec"b"*(vec"b" xx vec"c") + vec"b"*(vec"b" xx vec"a") + vec"b"*(vec"c" xx vec"c") - vec"b"*(vec"c" xx vec"a")`
= `vec"a"*(vec"b" xx vec"c") - 0 - 0 + 0 - 0 + 0 + 0 - vec"b"*(vec"c" xx vec"a")`
= `[vec"a", vec"b", vec"c"] - [vec"a", vec"b", vec"c"]` = 0
Hence proved.
APPEARS IN
संबंधित प्रश्न
If `bar"c" = 3bar"a" - 2bar"b"`, then prove that `[bar"a" bar"b" bar"c"] = 0`.
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"`
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"`
`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
If `hat"a", hat"b", hat"c"` are three unit vectors such that `hat"b"` and `hat"c"` are non-parallel and `hat"a" xx (hat"b" xx hat"c") = 1/2 hat"b"`, find the angle between `hat"a"` and `hat"c"`
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 `bar c = 3bara - 2barb` and `[bara barb + barc bara + barb + barc] = 0` then prove that `[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 `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 \[\overline{\mathrm{a}}=4\hat{\mathrm{i}}+3\hat{\mathrm{j}}+\hat{\mathrm{k}},\overline{\mathrm{b}}=\hat{\mathrm{i}}-2\hat{\mathrm{j}}+2\hat{\mathrm{k}}\] then \[\mathbf{\overline{a}}\times\left(\mathbf{\overline{a}}\times\left(\mathbf{\overline{a}}\times\mathbf{\overline{b}}\right)\right)=\]
