The angle between two vectors OA and ob is x, OA = 3, OB = 2, if the point m is on the straight line ob, and the minimum value of OA + OM (1) If θ = π / 3, find the value of vector OA · vector ab (2) If point m is on line ob, and the minimum value of | vector OA + vector om | is 3 / 2, find the value of X? Two questions

The angle between two vectors OA and ob is x, OA = 3, OB = 2, if the point m is on the straight line ob, and the minimum value of OA + OM (1) If θ = π / 3, find the value of vector OA · vector ab (2) If point m is on line ob, and the minimum value of | vector OA + vector om | is 3 / 2, find the value of X? Two questions

1. If | vector OA vector ab | & # 178; = | OA - (ob-oa) | & # 178; = | 2oa-ob | & # 178; = 4 | OA | & # 178; - 4oa * ob + ob | & # 178; = 36-12 + 4 = 28, then the module is 2 √ 7
2. Because the OM vector is on ob, let om = tob, then | OA + om | & # 178; = | OA | & # 178; + 2oa * om + om | & # 178; = 9 + 6tcosx + T & # 178; = [T + 3cosx] & # 178; + 9sin & # 178; X, then the minimum value of | OA + om | is 3sinx = 3 / 2, then SiNx = 1 / 2, then x = π / 6 or x = 5 π / 6