Advertisements
Advertisements
प्रश्न
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
Advertisements
उत्तर
Given `vec"a" xx (vec"b" xx vec"c") = lvec"a" + "m"vec"b" + "n"vec"c"`
`(vec"a"*vec"c")vec"b" - (vec"a"*vec"b")vec"c" = lvec"a" + "m"vec"b" + "n"vec"c"`
Compare ```vec"a", vec"b", vec"c"` on both sides
l = 0
m = `vec"a"*vec"c"`
n = `- (vec"a"*vec"b")`
m = 3 + 4 + 3, n = – (2 – 2 + 3)
m = 10, n = – 3
l = 0, m = 10, n = – 3
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`.
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 `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"`
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"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 `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 `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`
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 \[\mathbf{\overline{a}}\times\left(\mathbf{\overline{a}}\times\left(\mathbf{\overline{a}}\times\mathbf{\overline{b}}\right)\right)=\]
