If the vector `bar(b)=3hat j+4hat k` is written as the sum of vector `bar(b)_(1)` parallel to `bar(a)=hat i+hat j` and a vector `bar(b)_(2)` perpendicular to `bar(a)` then `bar(b)_(1)times bar(b)_(2)=`

The vector bar(b)=3bar(i)+4bar(k) is to be written as sum of a vector bar(b)_(1) parallel to bar(a)=bar(i)+bar(j) and a vector bar(b)_(2) perpendicular to bar(a) then bar(b)_(1) is equal to

Let bar(alpha) = 3hat(i) + hat(j) " and " bar(beta)=2hat(i) -hat(j)+3hat(k). "if "bar(beta)=bar(beta)_(1)-bar(beta)_(2) where bar(beta)_(1) is parallel to bar(alpha) and bar(beta)_(2) perpendicular to bar(alpha) then bar(beta)_(1)xx bar(beta)_(2) is equal to

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

Consider the vectors bar(a)=hat(i)-2hat(j)+hat(k) and bar(b)=4hat(i)-4hat(j)+7hat(k) . What is the vector perpendicular to both the vectors ?

If the vector -bar(i)+bar(j)-bar(k) bisects the angles between the vector bar(c) and the vector 3bar(i)+4bar(j) ,then the unit vector in the direction of bar(c) 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))

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

If the vectors bar(a)=2bar(i)+3bar(j)+6bar(k) and bar(b) are collinear and |bar(b)|=21 , then bar(b) equals to