Advertisements
Advertisements
Question
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`
Advertisements
Solution
`vec"a" xx vec"b"` is ⊥r to `vec"a"` and `vec"b"`
`vec"c" xx vec"d"` is ⊥r to `vec"c"` and `vec"d"`
Since `vec"a", vec"b", vec"c"` and `vec"d"` are coplanar.
`vec"a" xx vec"b", vec"c" xx vec"d"` are ⊥r to same plane
`vec"a" xx vec"b"` parallel to `vec"c" xx vec"d"`
⇒ `(vec"a" xx vec"b") xx (vec"c" xx vec"d") = vec0`
APPEARS IN
RELATED QUESTIONS
Prove that `[bar"a" bar"b" + bar"c" 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"`
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
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"`
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"`
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 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 `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]= 0 "then prove that" [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 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, `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 \[\mathbf{\overline{a}}\times\left(\mathbf{\overline{a}}\times\left(\mathbf{\overline{a}}\times\mathbf{\overline{b}}\right)\right)=\]
