[" 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=]

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

The vectors 2bar(i)-3bar(j)+bar(k), bar(i)-2bar(j)+3bar(k), 3bar(i)+bar(j)-2bar(k)

The vectors bar(i)+4bar(j)+6bar(k),2bar(i)+4bar(j)+3bar(k) and bar(i)+2bar(j)+3bar(k) form

The position vectors of three vertices in order of a parallelogram are respectively bar(i)+bar(j)+bar(k),bar(i)+3bar(j)+5bar(k) and 7bar(i)+9bar(j)+11bar(k) , then find out the position vector of its fourth vertex.

If bar(a)=bar(i)+4bar(j), bar(b)=2bar(i)-3bar(j) and bar(c)=5bar(i)+9bar(j)" then "bar(c)=

If bar(OP)=2bar(i)+3bar(j)-bar(k), bar(OQ)=3bar(i)-4bar(j)+2bar(k) then d.c's of bar(PQ) are

The points with P.V's bar(i)+2bar(j)+bar(k), 2bar(i)+3bar(j)+4bar(k) and 4bar(i)+5bar(j)+10bar(k) form

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 the points A,B,C are -2bar(i)+bar(j)-bar(k), -4bar(i)+2bar(j)+2bar(k), 6bar(i)-3bar(j)-13bar(k) respectively and bar(AB) = lambda bar(AC) then find the value of lambda .