If `bar(a)=(3hat i-hat j)/(sqrt(10)),bar(b)=(hat i+3hat j+hat k)/(sqrt(11)),` then the value of `(2bar(a)+bar(b))*[(bar(a)timesbar(b))times(bar(a)-3bar(b))]`

If bar(a)=(1)/(sqrt(10))(3hat(i)+hat(k)) and bar(b)=(1)/(7)(2hat(i)+3hat(j)-6hat(k)) then the value of (2bar(a)-bar(b)*((bar(a)timesbar(b))times(bar(a)+2bar(b))} is equal to

If bar(a)=hat i+hat j+2hat k, bar(b)=hat i+2hat j+2hat k and |bar(c)_(1)|=1 ,then the maximum value of [bar(a)timesbar(b) quad bar(b)timesbar(c) quad bar(c)timesbar(a)] is

If bar(a)=3hat i-3hat j-4hat k, bar(b)=hat i+2hat j+hat k and bar(c)=3hat i-hat j-2hat k , then [bar(a) bar(b) bar(c)] =

If bar(a)=3hat i+4hat j+5hat k then the value of (bar(a)timeshat i)^(2)+(bar(a)timeshat j)^(2)+(bar(a)timeshat k)^(2) is ......

If bar(a)=2hat i-hat j+2hat k then the value of |bar(a)timeshat i|^(2)+|bar(a)timeshat j|^(2)+|bar(a)timeshat k|^(2)=

Let bar(a)=3hat i+2hat j+2hat k,bar(b)=hat i+2hat j-2hat k Then a unit vector perpendicular to both bar(a)-bar(b) and bar(a)+bar(b) is

If bar(P)=hat i+hat j+hat k,bar(Q)=2hat i-hat j-hat k , then bar(P)-bar(Q) is

Let bar(a)=hat j-hat k and bar(c)=hat i-hat j-hat k then the vector bar(b) satisfying bar(a)timesbar(b)+bar(c)=0 and bar(a).bar(b)=3 is

Let bar(a)=3hat i+2hat j+2hat k , bar(b)=hat i+2hat j-2hat k .Then a unit vector perpendicular to both bar(a)-bar(b) and bar(a)+bar(b) is

Let bar(a)=2hat i+hat j-2hat k,bar(b)=hat i+hat j and bar(c) be a vector such that |bar(c)-bar(a)|=3,|(bar(a)timesbar(b))timesbar(c)|=3 and the angle between bar(c) and bar(a)timesbar(b) is 30^(@) . Then, bar(a).bar(c) is equal to