If `bar(a) = 2bar(i)+5bar(j)+bar(k), bar(b) = 4bar(i)+mbar(j)+nbar(k)` are collinear vectors then find m and n.

If bar(a) = 2bar(i)+5bar(j)+bar(k) and bar(b) = 4bar(i)+mbar(j)+nbar(k) are collinear vectors then find m,n.

IF bar(a)=2bar(i)+5bar(j)+bar(k),bar(b)=4bar(i)+mbar(j)+nbar(k) are collinear vectors then find m+n

If the vectors bar(a) = 2bar(i) -bar(j) + bar(k), bar(b) = bar(i) + 2bar(j)-3bar(k), bar(c ) = 3bar(i) + pbar(j) +5bar(k) are coplanar then find p.

If the vectors - 3 bar(i) + 4 bar(j) + lambda bar(k) and mu bar(i)+ 8 bar (j) + 6 bar(k) are collinear vectors, then find lambda and mu

If bar(a) = bar(i) + 2bar(j) + 3bar(k), bar(b) = 3bar(i) +5bar(j) -bar(k) are 2 sides of a triangle, find its area.

If bar(a) = 2bar(i) - 3bar(j) + 5bar(k), bar(b) = -bar(i) + 4bar(j) + 2bar(k) then find bar(a) xx bar(b) and unit vector perpendicular to both bar(a), bar(b) [-26bar(i) - 9bar(j) + 5bar(k), +- 1/(sqrt(782))26bar(i)+9bar(j)-5bar(k)) .

If bar(a) = 2bar(i) - bar(j) + bar(k), and bar(b) = bar(i) - 3bar(j) - 5bar(k) then find |bar(a) xx bar(b)| .

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.