The position vectors of the vertices `A ,B ,a n dC` of a triangle are ` hat i+ hat j , hat j+ hat ka n d hat i+ hat k` , respectively. Find the unite vector ` hat r` lying in the plane of `A B C` and perpendicular to `I A ,w h e r eI` is the incentre of the triangle.

The position vectors of vertices of a Delta ABC are 4hat(i)-2hat(j), hat(i)-3hat(k) and -hat(i)+5hat(j)+hat(k) respectively, then angle ABC is equal to

If the position vector of the vertices of a triangle are hat(i)-hat(j)+2hat(k), 2hat(i)+hat(j)+hat(k) & 3hat(i)-hat(j)+2hat(k) , then find the area of the triangle.

vec A B=3 hat i- hat j+ hat ka n d vec C D=-3 hat i+2 hat j+4 hat k are two vectors. The position vectors of the points Aa n dC are =6 hat i+7 hat j+4 hat ka n d=-9 hat j+2 hat k respectively. Find the position vector of a point P on the line A B and a point Q on the line C D such that vec P Q is perpendicular to vec A Ba n d vec C B both.

The position vectors of the points A,B,C are 2hat i+hat j-hat k,3hat i-2hat j+hat k and hat i+4hat j-hat k respectively.These pooints Form an isosceles triangle Form a right triangle Are collinear Form a scalene triangle

If vec a*hat i=vec a*(hat i+hat j)=vec a*(hat i+hat j+hat k) then find the unit vector vec a

If the position vectors of the point A and B are 3hat(i)+hat(j)+2hat(k) and hat(i)-2hat(j)-4hat(k) respectively. Then the eqaution of the plane through B and perpendicular to AB is

If vec a=hat i+hat j,vec b=hat j+hat k,vec c=hat k+hat i find the unit vector in the direction of vec a+vec b+vec c

Write a unit vector perpendicular to hat i+ hat j\ a n d\ hat j+ hat kdot