HSC Arts (English Medium) 12th Standard Board Exam - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

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

`"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 `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 `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 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`