If `bar(AB)=3bar(p)-bar(q) and bar(AD)=bar(p)-3bar(q)` are adjacent sides of a parallelogram ABCD where `|p|=2=|bar(q)|(bar(p),bar(q))=(pi)/(3)` then the length of the diagonal `bar(AC)` is

The adjacent sides of a parallelogram are 2bar(i)+4bar(j)-5bar(k) and bar(i)+2bar(j)+3bar(k) then the unit vector parallel to a diagonal is

If bar(c)=3bar(a)-2bar(b) , then prove that [bar(a)bar(b)bar(c)]=0 .

Vectors along the adjacent sides of parallelogram are bar(a)=bar(i)+2bar(j)+1bar(k),bar(b)=2bar(i)+4bar(j)+1bar(k) .Find length of longer diagonal of parallelogram

If bar(a)=2bar(m)+bar(n),bar(b)=bar(m)-2bar(n), Angle between the unitvectors bar(m) and bar(n) is 60^(@). a b are the sidesa parallelogram then the lengths of the diagonals are

The vectors bar(AB)=3bar(i)+4bar(k) and bar(AC)=5bar(i)-2bar(j)+4bar(k) are the sides of a triangle ABC .The length of the median through A

If bar(p)=bar(a)+bar(b),bar(q)=bar(a)-bar(b),|bar(a)|=|bar(b)|=r , then |bar(p)timesbar(q)| =

A parallelogram is constructed on 2bar(a)+3bar(b) and 3bar(a)-5bar(b), where ।bar(a)|=4 and |bar(b)|=5. If the angle between bar(a) and bar(b) is (pi)/(3), then the magnitude of the smaller diagonal is

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

If bar(a)=bar(i)+bar(j)+bar(k) , bar(b)=bar(i)+2bar(j)+3bar(k) then a unit vector perpendicular to both vectors (bar(a)+bar(b)) and (bar(a)-bar(b)) is