हिंदी

If r=xi+yj+zk ,find (r x i).( r x j)+xy - Mathematics

Advertisements
Advertisements

प्रश्न

If `vecr=xhati+yhatj+zhatk` ,find `(vecrxxhati).(vecrxxhatj)+xy`

उत्तर

Given

`vecr=xhati+yhatj+zhatk`

`(vecrxxhati).(vecrxxhatj)+xy`

`=[(xhati+yhatj+zhatk)xxhati].[(xhati+yhatj+zhatk)xxhatj]+xy`

`=[(xhatixxhati+yhatjxxhati+zhatkxxhati)].[(xhatixxhatj+yhatjxxhatj+zhatkxxhatj)]+xy`

`=(0hati-yhatk+zhatj).(xhatk+0hatj-zhati)+xy`

`=(0z-xy+0z)+xy`

`=-xy+xy`

`=0`

shaalaa.com
Vectors Examples and Solutions
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
2014-2015 (March) Delhi Set 1

संबंधित प्रश्न

If a unit vector `veca` makes angles `pi/3` with `hati,pi/4` with `hatj` and acute angles θ with ` hatk,` then find the value of θ.


Write the value of `vec a .(vecb xxveca)`


If `veca=hati+2hatj-hatk, vecb=2hati+hatj+hatk and vecc=5hati-4hatj+3hatk` then find the value of `(veca+vecb).vec c`


 

If `veca=2hati+hatj+3hatk and vecb=3hati+5hatj-2hatk` ,then find ` |veca xx vecb|`

 

Using vectors find the area of triangle ABC with vertices A(1, 2, 3), B(2, −1, 4) and C(4, 5, −1).


Find the angle between the vectors `vec"a" + vec"b" and  vec"a" -vec"b" if  vec"a" = 2hat"i"-hat"j"+3hat"k" and vec"b" = 3hat"i" + hat"j"-2hat"k", and"hence find a vector perpendicular to both"  vec"a" + vec"b" and vec"a" - vec"b"`.


Find the angle between the vectors `2hat"i" - hat"j" + hat"k"` and `3hat"i" + 4hat"j" - hat"k"`.


Using vectors, find the area of the triangle ABC with vertices A(1, 2, 3), B(2, – 1, 4) and C(4, 5, – 1).


Using vectors, prove that the parallelogram on the same base and between the same parallels are equal in area.


Show that area of the parallelogram whose diagonals are given by `vec"a"` and `vec"b"` is `(|vec"a" xx vec"b"|)/2`. Also find the area of the parallelogram whose diagonals are `2hat"i" - hat"j" + hat"k"` and `hat"i" + 3hat"j" - hat"k"`.


The value of λ for which the vectors `3hat"i" - 6hat"j" + hat"k"` and `2hat"i" - 4hat"j" + lambdahat"k"` are parallel is ______.


The vectors from origin to the points A and B are `vec"a" = 2hat"i" - 3hat"j" + 2hat"k"` and `vec"b" = 2hat"i" + 3hat"j" + hat"k"`, respectively, then the area of triangle OAB is ______.


For any vector `vec"a"`, the value of `(vec"a" xx hat"i")^2 + (vec"a" xx hat"j")^2 + (vec"a" xx hat"k")^2` is equal to ______.


If `|vec"a"|` = 10, `|vec"b"|` = 2 and `vec"a".vec"b"` = 12, then value of `|vec"a" xx vec"b"|` is ______.


The vectors `lambdahat"i" + hat"j" + 2hat"k", hat"i" + lambdahat"j" - hat"k"` and `2hat"i" - hat"j" + lambdahat"k"` are coplanar if ______.


If `|vec"a"|` = 4 and −3 ≤ λ ≤ 2, then the range of `|lambdavec"a"|` is ______.


If `|vec"a" xx vec"b"|^2 + |vec"a".vec"b"|^2` = 144 and `|vec"a"|` = 4, then `|vec"b"|` is equal to ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×