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

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

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) .

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

Find the unit vector in the direction of the sum of the vectors bar(a) = 2bar(i)+ 2bar(j) - 5bar(k) and bar(b) = 2bar(i) + bar(j) + 3bar(k) .

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

Find unit vector perpendicular to both bar(i) + bar(j) + bar(k) and 2bar(i) + bar(j) + 3bar(k) .

bar (a) = 2bar (i) + 3bar (j) -bar (k), bar (b) = bar (i) + 2bar (j) -4bar (k), bar (c) = bar (i) + bar (j) + bar (k), bar (d) = bar (i) -bar (j) -bar (k) then