Because the beginners of vector, not very skilled. Hope enthusiastic friends can solve every step of the process (all letters represent vectors) 1、 AB + BC + Ca 2、 AB + MB + Bo + OM 3、 AB-AC + bd-cd 4、 OA + OC + Bo + CO Also, my vector operation is very slow, and the accuracy is very low. How can I carry out vector operation quickly and accurately?

Because the beginners of vector, not very skilled. Hope enthusiastic friends can solve every step of the process (all letters represent vectors) 1、 AB + BC + Ca 2、 AB + MB + Bo + OM 3、 AB-AC + bd-cd 4、 OA + OC + Bo + CO Also, my vector operation is very slow, and the accuracy is very low. How can I carry out vector operation quickly and accurately?

Addition: end to end. For example: one = AC + Ca = 0 (vector) two = Ao + MB + om = am + MB = AB four = CO + OC + Bo + OA = Ba
Subtraction: common starting point, end point, direction to be subtracted. For example: three = CB + bd-cd = DB + BD = 0 (vector)

Triangle ABC and a point O, satisfy vector: oa2 + BC2 = ob2 + Ca2 = oc2 + AB2 (all above are squares, vector direction is in alphabetical order), find out what center O is triangle

O is the center of gravity of the triangle, from oa2 + BC2 = ob2 + Ca2 → oa2 + bc2-ob2-ca2 = 0 → 2 OC times AB = 0
In the same way, we deduce OA ⊥ BC, ob ⊥ Ca, so point O is the center of gravity of the triangle

Vector calculation in senior one
Given 3A + 4B + 5C = 0 (a, B, C are vectors), and | a | = | B | = | C | = 1, find the value of a · (B + C)

From 3A + 4B + 5C = 0,
→5c=3a+4b
→ 25 * C ^ 2 = 9 * a ^ 2 + 16 * B ^ 2 + 24a. B (the last A.B is dot product)
→a.b=0
Then the original formula is transformed into - 4B = 3A + 5C
→16*b^2=9a^2+25c^2+30a.c
→a.c=-0.6
∴a.(b+c)=ab+ac=-0.6