Question

101. If the vector b = 3j +4k is written as the sum of a vector b1
parallel to a=i+j and a vector b2 , perpendicular to vector a
then b1*b2 is equal to​

Answer 1

Answer:

from here the dot or cross product can be found easily......as it was not clear b1*b2 means dot or cross product

Answer 2

If the vector b = 3j +4k is written as the sum of a vector b₁ parallel to a=i+j and a vector b₂ , perpendicular to vector a  then b₁*b₂ is equal to $\frac{3}{2}(i+j)$

b = u + v   ...(1)

u =λ(i+j)  .....Parallel

A.v = 0   ....Perpendicular

(i+j),(xi+yj+zk) = 0

x = - y

so v =xi -xj +zk

from (1)

3j +4k = λ(i+j) + (xi -xj +zk)

so compairing gives,

λ= 3/2

Therefore,

b₁*b₂ is equal to $\frac{3}{2}(i+j)$