Whenever j and k are positive integers such that `(sqrt3)^(j) = 27^(k)` , what is the value of `j/k`?

If 3j-(k_5)=16-4k , what is the value of j+k ?

If (2)/(3)j-(1)/(4)k=(5)/(2) , what is the value of 8j-3k ?

What is value of i.i = j.j = k.k ?

If a and b are vectors such that |a+b|=sqrt(29) and a xx(2i+3j+4k)=(2i+3j+4k)xx b, then a possivalue of (a+b)*(-7i+2j+3k) is

Consider the equation k = 7/5 j + 54 . For what value of j is the value of k equal to 40 ?

Find the value of lambda , if the point with position vectors 3hat(i) - 2hat(j) - hat(k), 2hat(i) + 3hat(j) - 4hat(k), -hat(i) + hat(j) + 2hat(k) and 4hat(i) + 5hat(j) + lambda hat(k) are coplanar.

Find the value of lamda , if the points with position vectors 3hat(i)- 2hat(j)- hat(k), 2hat(i) + 3hat(j)- 4hat(k), -hat(i) + hat(j) + 2hat(k), 4hat(i) + 5hat(j) + lamda hat(k) are coplanar.

Find the value of lambda for which the four points with position vectors - hat j- hat k ,4 hat i+5 hat j+lambda hat k ,3 hat i+9 hat j+4 hat k and 4 hat i+4 hat j+4 hat k are coplanar.

If the position vectors of A and B are 3i - 2j + k and 2i + 4j - 3k then |vec(A)B|

A non-zero vector vec a is such that its projections along vectors (hat i+hat j)/(sqrt(2)),(-hat i+hat j)/(sqrt(2)) and hat k are equal,then unit vector along vec a is (sqrt(2)hat j-hat k)/(sqrt(3))b(hat j-sqrt(2)hat k)/(sqrt(3)) c.(sqrt(2))/(sqrt(3))hat j+(hat k)/(sqrt(3))d.(hat j-hat k)/(sqrt(2))