Let `a_j=7/4(2/3)^(j-1),j in N` If `b_j=a_j^2+a_j`. sum of the infinite series formed by `b_1's` is `(10 + alpha)` where `[1/alpha]`is equal to ([ ] represent greatest integer function)

Let a _(j) = (7)/(4) ((2)/(3)) ^( j -1), j in N . lf b _(j) = a _(j) ^(2) + a _(j), sum of the infinite sereies formed by b _(j) 's is (10 + alpha ) where [ (1)/( alpha ) ] is equal to ([] represent greatest integer function)

The projection of the vector 2i + aj - k on the vector i - 2j + k is (-5)/(sqrt(6)) . Then, the value of a is equal to

sum_(i = 1)^n sum_(j = 1)^i sum_(k = 1)^j 1 is equal to

If the vector 8i + aj of magnitude 10 is in the direction of the vector 4i + 3j, then the value of a is equal to a)6 b)3 c)-3 d)-6

What is the condition for the vectors 2i+3j-4k and 3i-aj+ bk to be parallel?