If `overset(to)(a) = (hat(i) + hat(j) + hat(k)) , overset(to)(a) , overset(to)(b) , overset(to)(c ) =1 " and " overset(to)(a) xx overset(to)(b) = hat(j) - hat(k), " then " overset(to)(b)` is equal to

If overset(to)(a) = (hat(i) + hat(j) + hat(k)) , overset(to)(a) .overset(to)(b) =1 " and " overset(to)(a) xx overset(to)(b) = hat(j) - hat(k), " then " overset(to)(b) is equal to

If overset(to)(A) = 2hat(i) + hat(k) , overset(to)(B) = hat(i) + hat(j) +hat(k) " and " overset(to) (C ) = 4hat(i) - 3hat(j) +7hat(k) Determine a vector overset(to)(R ) " satisfying " overset(to)(R ) xx overset(to)( B) = overset(to)( C ) xx overset(to)( B) " and " overset(to)(R ) " ." overset(to)(A) = 0

Let overset(to)(a) =2hat(i) + hat(j) -2hat(k) " and " overset(to)(b) = hat(i) + hat(j) . " If " overset(to)(c ) is a vectors such that |overset(to)(a)"." overset(to)(c ) = |overset(to)( c)| , |overset(to)(c )- overset(to)(a)|= 2sqrt(2) and the angle between (overset(to)(a) xx overset(to)(b)) " and " overset(to)( c ) " is " 30^(@), " then "|(overset(to)(a) xx overset(to)(b)) xx overset(to)( c )| is equal to

If overset(to) (a) = hat(i) + 2 hat(j) + hat(k) and overset(to)(b) = hat(i) - 2 hat(j) - 3 hat(k) then ( overset(to)(a) + overset(to)(b) ). ( overset(to)(a) - overset(to)(b) ) = …......

If overset(to)(a) " and " overset(to)(b) are vectors in space given by overset(to)(a) = (hat(i) -2hat(j))/(sqrt(5)) " and " overset(to)(b) = (2hat(i) + hat(j) +3hat(k))/(sqrt(14)) then the value of (2overset(to)(a) + overset(to)(b)).[(overset(to)(a) xx overset(to)(b)) xx (overset(to)(a) -2overset(to)(b))] is .........

Let overset(to)(a) = hat(i) - hat(j) , overset(to)(b) - hat(k) , overset(to)( c) - hat(k) - hat(i) . If overset(to)(d) is a unit vector such that overset(to)(a) , Overset(to)(d) =0= [ overset(to)(b) overset(to)(c ) overset(to)d)] then overset(to)(d) equals

Let overset(to)(a) =2hat(i) +hat(j) + hat(k), overset(to)(b) =hat(i) + 2hat(j) -hat(k) and a unit vector overset(to)(c ) be coplanar. If overset(to)(c ) is perpendicular to overset(to)(a) " then " overset(to)(c ) is equal to

If overset(to)(a) =hat(i) - hat(k) , overset(to)(b) = x hat(i) + hat(j) + (1-x) hat(k) and overset(to)(c ) =y hat(i) +x hat(j) + (1+x-y) hat(k) . "Then " [overset(to)(a) , overset(to)(b) , overset(to)( c) ] depends on

Let overset(to)(a) = hat(i) - hat(j) , vecb=-hat(j) - hat(k) , overset(to)( c) =- hat(i) - hat(k) . If overset(to)(d) is a unit vector such that overset(to)(a).vec(d) =0= [ vec(b) vec(c ) vecd] then overset(to)(d) equals

Let overset(to)(a) =hat(i)+2hat(j)+hat(k),overset(to)(b) =hat(i)-hat(j)+hat(k),overset(to)(C )=hat(i)+hat(j) -hat(k). A vector coplanar to overset(to)(a) and overset(to)(b) has a projections along overset(to)(c ) of magnitude (1)/(sqrt(3)) then the vector is