Thread: dot/cross product rules

Just asking for some tips for answering questions, such as:
1)Find a such that i-4k is perpendicular to the vector -3i + ak
2)Suppose x and y are vectors which are linearly independent and the following vector equation holds for some scalars a and b: 9x + a(x+y) = b(x-2y). Find a and b.
3)Suppose x and y are vectors which are linearly independent and the following vector equation holds for some scalars a and b: -4x + a(x+y) = b(x-3y). Find a and b.

Thanks for any help

i) Two vectors are perpendicular when their dot product is 0.

ii) Expand, collect like terms, and equate the coefficients of x and the coefficients of y.

iii) See ii).