HSC Science Class 12 - Tamil Nadu Board of Secondary Education Question Bank Solutions for Mathematics

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"`

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"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"`

`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", vec"b", vec"c", vec"d"` are coplanar vectors, show that `(vec"a" xx vec"b") xx (vec"c" xx vec"d") = vec0`

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

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"`

Evaluate the following limits, if necessary use l’Hôpital Rule:

`lim_(x -> 0) (1 - cosx)/x^2`

Evaluate the following limits, if necessary use l’Hôpital Rule:

`lim_(x - oo) (2x^2 - 3)/(x^2 -5x + 3)`

Evaluate the following limits, if necessary use l’Hôpital Rule:

`lim_(x -> oo) x/logx`

Evaluate the following limits, if necessary use l’Hôpital Rule:

`lim_(x -> x/2) secx/tanx`

Evaluate the following limits, if necessary use l’Hôpital Rule:

`lim_(x -> oo) "e"^-x sqrt(x)`

Evaluate the following limits, if necessary use l’Hôpital Rule:

`lim_(x -> 0) (1/sinx - 1/x)`

Evaluate the following limits, if necessary use l’Hôpital Rule:

`lim_(x -> 1^+) (2/(x^2 - 1) - x/(x - 1))`

Evaluate the following limits, if necessary use l’Hôpital Rule:

`lim_(x -> 0^+) x^x`

Evaluate the following limits, if necessary use l’Hôpital Rule:

`lim_(x -> oo) (1 + 1/x)^x`

Evaluate the following limits, if necessary use l’Hôpital Rule:

`lim_(x -> pi/2) (sin x)^tanx`