Find the value of `[bar(i)+bar(j)+bar(k),bar(i)-bar(j),bar(i)+2bar(j)-bar(k)]`.

Find the volume of the tetrahedron having the edges , bar(i) + bar(j) + bar(k), bar(i)-bar(j), bar(i) + 2bar(j) + bar(k) .

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

Find the position vector of the centroid of the tetrahedron formed by the points 2bar(i)-bar(j)-3bar(k), 4bar(i)+bar(j)+3bar(k), 3bar(i)+2bar(j)-bar(k), bar(i)+4bar(j)+2bar(k) .

Find the vector area and area of the triangle with vertices bar(i) + bar(j)-bar(k), 2bar(i)- 3bar(j) + bar(k), 3 bar(i) + bar(j)- 2bar(k) .

Show that the following vectors are linearly dependent i) bar(i)+bar(j)+2bar(k), bar(j)+2bar(k), bar(i)+2bar(j)+4bar(k)

Find t, for which the vectors 2bar(i) - 3bar(j) + bar(k), bar(i) + 2bar(j) -3bar(k) , bar(j) - tbar(k) are coplanar.

If the volume of the tetrahedron with edges 2bar(i)+bar(j)+bar(k),bar(i)+abar(j)+bar(k) and vec i+2bar(j)-bar(k) is one cubic unit then a=

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.

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