Let two non-zero vectors E1 and E2. ① try to determine the real number k so that Ke1 + E2 and E1 + Ke2 are collinear. ② if | E1 | = 2, | E2 | = 3, the angle between E1 and E2 is 60 °, try to determine K so that Ke1 + E2 and E1 + Ke2 are perpendicular

Let two non-zero vectors E1 and E2. ① try to determine the real number k so that Ke1 + E2 and E1 + Ke2 are collinear. ② if | E1 | = 2, | E2 | = 3, the angle between E1 and E2 is 60 °, try to determine K so that Ke1 + E2 and E1 + Ke2 are perpendicular

(1) k=1
(2) E1 · E2 = 3 / 2, so k = - 1 / 3 or - 3

It is known that E 1 and E 2 are not collinear. To make Ke 1 + E 2 and E 1 + Ke 2 collinear, find the value of K

To be collinear, let Ke1 + E2 = m (E1 + Ke2) m ≠ 0
So Ke1 + E2 = ME1 + kme2
That is, (K-M) e1 = (KM-1) E2
Because E1 and E2 are not collinear,
So K-M = 0; KM-1 = 0;
If we solve this system of equations, we get k = 1 or - 1