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" + 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`.
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.
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")`
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"b" * vec"c")vec"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" = 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")` = ?
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"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"]` = ______.
Let three vectors `veca, vecb` and `vecc` be such that `vecc` is coplanar with `veca` and `vecb, vecc,` = 7 and `vecb` is perpendicular to `vecc` where `veca = -hati + hatj + hatk` and `vecb = 2hati + hatk`, then the value of `2|veca + vecb + vecc|^2` is ______.
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 `barc= 3bara - 2barb and [bara barb+barc bara+barb+barc] = "then proved" [bara barb barc] = 0`
If `bar c = 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`
