HSC Arts Class 11 - Tamil Nadu Board of Secondary Education Question Bank Solutions for Mathematics

Verify whether the following ratios are direction cosines of some vector or not

`1/5, 3/5, 4/5`

Verify whether the following ratios are direction cosines of some vector or not

`1/sqrt(2), 1/2, 1/2`

Verify whether the following ratios are direction cosines of some vector or not

`4/3, 0, 3/4`

Find the direction cosines of a vector whose direction ratios are
1, 2, 3

Find the direction cosines of a vector whose direction ratios are

`1/sqrt(2), 1/2, 1/2`

Find the direction cosines of a vector whose direction ratios are
0, 0, 7

Find the direction cosines and direction ratios for the following vector

`3hat"i" - 4hat"j" + 8hat"k"`

Find the direction cosines and direction ratios for the following vector

`3hat"i" + hat"j" + hat"k"`

Find the direction cosines and direction ratios for the following vector

`hat"j"`

Find the direction cosines and direction ratios for the following vector

`5hat"i" - 3hat"j" - 48hat"k"`

Find the direction cosines and direction ratios for the following vector

`3hat"i" - 3hat"k" + 4hat"j"`

Find the direction cosines and direction ratios for the following vector

`hat"i" - hat"k"`

A triangle is formed by joining the points (1, 0, 0), (0, 1, 0) and (0, 0, 1). Find the direction cosines of the medians

If `1/2, 1/sqrt(2), "a"` are the direction cosines of some vector, then find a

If (a, a + b, a + b + c) is one set of direction ratios of the line joining (1, 0, 0) and (0, 1, 0), then find a set of values of a, b, c

If `vec"a" = 2hat"i" + 3hat"j" - 4hat"k", vec"b" = 3hat"i" - 4hat"j" - 5hat"k"`, and `vec"c" = -3hat"i" + 2hat"j" + 3hat"k"`,  find the magnitude and direction cosines of `vec"a", vec"b", vec"c"`

If `vec"a" = 2hat"i" + 3hat"j" - 4hat"k", vec"b" = 3hat"i" - 4hat"j" - 5hat"k"`, and `vec"c" = -3hat"i" + 2hat"j" + 3hat"k"`,  find the magnitude and direction cosines of `3vec"a"- 2vec"b"+ 5vec"c"`

Choose the correct alternative:
The unit vector parallel to the resultant of the vectors `hat"i" + hat"j" - hat"k"` and `hat"i" - 2hat"j" + hat"k"` is

Integrate the following functions with respect to x :

`(x^3 + 4x^2 - 3x + 2)/x^2`

Integrate the following functions with respect to x :

`[sqrt(x) + 1/sqrt(x)]^2`