Let `bar(u)=hat i+hat j, bar(v)=hat i-hat j,bar(w)=hat i+2hat j+3hat k`, n unit vector such that `bar(u).bar(n)=0,bar(v).bar(n)=0` then `|bar(w).bar(n)|` =

Let bar(u)=bar(i)+bar(j),bar(v)=bar(i)-bar(j),bar(w)=bar(i)+2bar(j)+3bar(k) .If bar(n) is a unit vector such that bar(u).bar(n)=0,bar(v).bar(n)=0 then |bar(w).bar(n)|=

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)=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)=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)=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)] =

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

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

If bar(a)=hat i+2hat j-hat k and bar(b)=3hat i+hat j-5hat k find a unit vector in a direction parallel to vector (bar(a)-bar(b))

Let bar(a)=4hat i+3hat j-hat k,bar(b)=5hat i+2hat j+2hat k,bar(c)=2hat i-2hat j)-3hat k and bar(d)=4hat i-4hat j+3hat k; prove that bar(b)-bar(a) and bar(d)-bar(c) are parallel and find the ratio of their moduli.

Let vec(u) = hat(i) + hat(j), vec(v) = hat(i) - hat(j) and vec(w) = hat(i) + 2hat(j) + 3hat(k) . If hat(n) is a unit vector such that vec(u).vec(n) = 0 and vec(v).hat(n) = 0 then |vec(w).hat(n)| is equal to.