а) вектор a_x = 3i,
б) a*i = (3i+2j)*i = 3i*i + 2j*i = 3*1+2*0 = 3,
в) a_x = 3,
г) a*b = (3i+2j)*(2i-j) = (3i+2j)*(2i) + (3i+2j)*(-j) = 2i*(3i+2j) - j*(3i+2j) =
= 6i*i+4i*j - 3j*i -2j*j = 6+0-0-2 = 4.
д) (a+b)*(a-2b) = ( 3i+2j + 2i - j )*( 3i+2j - 2*(2i -j) ) = ( 5i+j )*( 3i + 2j - 4i + 2j) =
= ( 5i+j )*( -i+4j ) = ( 5i+j)*(-i) + (5i+j)*(4j) = -i*(5i+j) + 4j*(5i+j) = -5i*i - i*j + 20j*i+4j*j =
= -5 - 0 + 0 + 4 = -1.
