A unit vector coplanar with `bar(i)+bar(j)-bar(k)` and `bar(i)-2bar(j)+bar(k)` and perpendicular to `bar(i)+bar(j)+bar(k)` is

Let bar(a) be a unit vector bar(b)=2bar(i)+bar(j)-bar(k) and bar(c)=bar(i)+3bar(k) then maximum value of [bar(a)bar(b)bar(c)] is

Let bar(a) be a unit vector bar(b)=2bar(i)+bar(j)-bar(k) and bar(c)=bar(i)+3bar(k) then maximum value of [[bar(a),bar(b),bar(c)]] is

If the volume of tetrahedron with edges bar(i)+bar(j)-bar(k) , bar(i)+abar(j)+bar(k) and bar(i)+2bar(j)-bar(k) is (a)/(6) then a=

If p=bar(i)+abar(j)+bar(k) and q-bar(i)+bar(j)+bar(k) then |bar(p)+bar(q)|=|bar(p)|+|bar(q)| is true for

If p=bar(i)+abar(j)+bar(k) and q=bar(i)+bar(j)+bar(k) then |bar(p)+bar(q)|=|bar(p)|+|bar(q)| is true for

In a triangle ABC ,right angled at the vertex A ,if the position vectors of A, B and C are respectively 3bar(i)+bar(j)-bar(k), -bar(i)+3bar(j)+pbar(k) and 5bar(i)+qbar(j)-4bar(k), then the points (p,q) lies on a line

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 reciprocal of bar(a) where bar(a)=-bar(i)+bar(j)+bar(k),bar(b)=bar(i)-bar(j)+bar(k),bar(c)=bar(i)+bar(j)+bar(k) is

The vector equation of the plane passing through the points bar(i)-2bar(j)+bar(k),3bar(k)-2bar(j) and parallel to the vector 2bar(i)+bar(j)+bar(k) is

The orthogonal projection of bar(a)=2bar(i)+3bar(j)+3bar(k) on bar(b)=bar(i)-2bar(j)+bar(k) (where bar(i)*bar(j)*bar(k) are unit vectors along there mutually perpendicular directions is