Advertisements
Advertisements
प्रश्न
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"`
Advertisements
उत्तर
`vec"a" xx vec"b" = |(hat"i", hat"j", hat"k"),(1, -2, 3),(2, 1, -2)|`
= `hat"i"(4 - 3) - hat"j"(- 2 - 6) + hat"k"(1 + 4)`
= `hat"i" + 8hat"j" + 5hat"k"`
`vec"a" xx vec"b" xx vec"c" = |(hat"i", hat"j", hat"k"),(1, 8, 5),(3, 2, 1)|`
`hat"i"(8 - 10) - hat"j"(1 - 15) + hat"k"(2 - 24)`
= `- 2hat"i" + 14hat"j" - 22hat"k"`
APPEARS IN
संबंधित प्रश्न
Prove that `[bar"a" bar"b" + bar"c" 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 `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"`
`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" = 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 = ?
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 `veca = hati + 2hatj + 3hatk, vecb = 2hati + 3hatj + hatk, vecc = 3hati + hatj + 2hatk` and `αveca + βvecb + γvecc = -3(hati - hatk)`, then the ordered triplet (α, β, γ) is ______.
If `bar c = 3bara - 2barb` and `[bara barb + barc bara + barb + barc] = 0` then prove that `[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`, then prove that `[bara barb barc]` = 0.
If, `barc = 3bara - 2barb`, then prove that `[bara barb barc] = 0`
Let `bara, barb and barc` be non-zero vectors such that `(bara xx barb) xx barc = 1/3 |barb||barc|bara`. If θ is the acute angle between the vectors `barb and barc`, then sinθ equals
