The position vectors of `A, B, C` are `bar i+bar j+bar k` ,`4 bar i+bar j+bar k` , `4 bar i+5 bar j+bar k` then the position vector of the circumcenter of the triangle ABC is -- Hint:- `s=((x_1+x_2)/2,(y_1+y_2)/2,z_1)`

If the position vectors of A, B, C, D are 3bar(i)+2bar(j)+bar(k), 4bar(i)+5bar(j)+5bar(k), 4bar(i)+2bar(j)-2bar(k), 6bar(i)+5bar(j)-bar(k) respectively then the position vector of the point of intersection of lines AB and CD is

If the position vectors of A, B are 2bar(i)-9bar(j)-4bar(k), 6bar(i)-3bar(j)+8bar(k) then the unit vector in the direction of vec(AB) is

The position vectors of the vertices of a triangle are 3bar(i)+4bar(j)+5bar(k),bar(i)+7bar(k) and 5bar(i)+5bar(j) The distance between the circumcentre and orthocentre is

If the position vectors of A,B and C are respectively 2bar(i)-bar(j)+bar(k),bar(i)+3bar(j)-5bar(k) and 3bar(i)-4bar(j)-4bar(k) then cos^(2)A=

The points whose position vectors are 2bar(i)+3bar(j)+4bar(k), 3bar(i)+4bar(j)+2bar(k) and 4bar(i)+2bar(j)+3bar(k) are the vertices of

If position vectors of points P,Q,R are bar(i)+4bar(j)-2bar(k),2bar(i)+bar(j)-2bar(k),quad -5bar(j)+bar(k) respectively then the distance from P to QR is

If bar(a) = bar(i) - bar(j)-bar(k), bar(b) = 2bar(i) - 3bar(j) + bar(k) then find the projection vector of bar(b) on bar(a) and its magnitude.

If bar(a) = bar(i) + bar(j)+bar(k), bar(b) = 2bar(i) + 3bar(j) + bar(k) then find the projection vector of bar(b) on bar(a) and its magnitude.