A triangle `O A B` is determined by the vectors ` vec aa n d vec b` as shown if fig. Show that the triangle has the area `` given by `1/2sqrt(|a|^2|b|^2-(a.b)^2)dot`

If the angel between unit vectors vec aa n d vec b60^0 , then find the value of | vec a- vec b|dot

For any vector vec a\ a n d\ vec b prove that | vec a+ vec b|lt=| vec a|+| vec b|dot

What is the angle between vectors vec a\ a n d\ vec b with magnitudes 2 and 3 respectively ? Given vec adot vec b=sqrt(3) .

Find the angle between two vectors vec aa n d vec b with magnitudes sqrt(3) and 2 respectively and such that vec adot vec b=sqrt(6.)

The vertices A , B , C of triangle A B C have respectively position vectors vec a , vec b , vec c with respect to a given origin O . Show that the point D where the bisector of /_A meets B C has position vector vec d=(beta vec b+gamma vec c)/(beta+gamma), where beta=| vec c- vec a| and, gamma=| vec a- vec b|dot

Find the angle between two vectors vec a\ a n d\ vec b with magnitudes 1\ a n d\ 2 respectively and when | vec axx vec b|=sqrt(3)dot

The vertices A , B , C of triangle A B C have respectively position vectors vec a , vec b , vec c with respect to a given origin O . Show that the point D where the bisector of /_A meets B C has position vector vec d=(beta vec b+gamma vec c)/(beta+gamma), where beta=| vec c- vec a| and, gamma=| vec a- vec b|dot Hence, deduce that incentre I has position vector (alpha vec a+beta vec b+gamma vec c)/(alpha+beta+gamma) where alpha=| vec b- vec c|

For any two vectors vec a and vec b , show that : ( vec a+ vec b)dot( vec a- vec b)=0, when | vec a|=| vec b|dot

In a triangle OAC, if B is the mid point of side AC and vec O A= vec a ,\ vec O B= vec b ,\ then what is vec O C ?

If vec a\ a n d\ vec b are unit vectors then write the value of | vec axx vec b|^2+( vec adot vec b)^2dot