Given the vector a = (2. K). B = (3. 4), and a is perpendicular to B, then the real number k =?

Given the vector a = (2. K). B = (3. 4), and a is perpendicular to B, then the real number k =?

Because a is perpendicular to B, a times b = 0
SO 2 * 3 + 4 * k = 0
k=-1.5

Given that vector a = (3,0,1), vector b = (k, 2, - 1) and = 3 π / 4, then the value of real number k is

∵=3π/4
∴COS=-（√2）/2
∵COS=（a·b）/（|a|·|b|）
The numerical value is brought in and simplified to 2K ^ 2-3k-12 = 0
The solution is K1 = (3 + √ 105) / 4
k2==（3-√105）/4

As shown in the figure, in △ ABC, point O is the midpoint of BC, and the lines passing through point O intersect the lines AB and AC at two different points m and N. if AB = mam, AC = Nan, find the value of M + n

Lengthen Ao to a 'to make Ao = a'o, lengthen a'c to intersect Mn at M', as shown in the figure: then △ OBM ≌ △ OCM ',' BM = cm ', ∫ Nam ∽ NCM', ∫ ncan = cm'am, namely AC − Anan = am − ABAM, ∫ AB = mam, AC = Nan, ∫ ab | = m | am |, | AC | = n | an |, substituting into the above formula, n-1 = 1-m, then M + n = 2

As shown in the figure, in △ ABC, D is the midpoint on the edge of BC, F and E are the points on AD and its extension respectively, CF ‖ be
(1) Verification: △ BDE ≡ CDF
(2) Please connect BF and CE, try to judge what kind of special quadrilateral becf is, and explain the reason

As shown in the figure, in △ ABC, D is the midpoint of BC side, F and E are the points on AD and its extension line respectively, CF ‖ be. (1) verification: △ BDE ≌ △ CDF; (2) please connect BF and CE, try to judge what kind of special quadrilateral becf is, and explain the reason; (3) under (2), if becf is diamond, then △ ABC should meet what conditions