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)=

If bar(a) is any vector the value of hat i times(bar(a)times hat i)+hat j times(bar(a)times hat j)+hat k times(bar(a)times hat k)=

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

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)=(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)=(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))]

hat(i)*(hat(j)timeshat(k))+hat(j)*(hat(k)timeshat(i))+hat(k)*(hat(i)timeshat(j))=

If bar(a) and bar(b) are vectors such that |bar(a)+bar(b)|=sqrt(29) and bar(a)times(2hat i+3hat j+4hat k)=(2hat i+3hat j+4hat k)timesbar(b) then the value of (bar(a)+bar(b)).(-7hat i+2hat j+3hat k) is .......

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

If overline(a)*hat(i)=4, then (overline(a)timeshat(j))*(2hat(j)-3hat(k))=