Question

Помогите упростить выражение( векторы)а) ( векторы) FK + MQ + KP + AM + QK + PFб) ( векторы) AD + MP + EK - EP - MDв)( векторы) AC - BC - PM - AP + BM

Answer 1

а)  FK + MQ + KP + AM + QK + PF=AM+MQ+QK+KP+PF+FK=AK

б)  AD + MP + EK - EP - MD=AD+(EK-EP)+(MP-MD)=AD+PK+DP=

=AD+DP+PK=AK

в)  AC - BC - PM - AP + BM=(AC-BC)-(AP+PM)+BM=

=AC-BC-(AP+PM)+BM=AC-BC-AM+BM=(AC-AM)+(BM-BC)=

=MC+CM=MM=0

Answer 2

а)Группируем:

(FK+KP) + PF +(MQ+QK) + AM = FP + PF + MK + AM = 0 + (AM + MK) = AK .

 

б) Аналогично:

...= (AD + DM) + MP + (PE + EK) = (AM + MP) + PK = AK.

 

в)...= (AC + CB) + (BM + MP) + PA = AP + PA = 0 

Answer 3

Simplifying the Expression with Vectors

To simplify the given expression involving vectors, we will break it down into smaller parts and apply vector addition and subtraction rules.

a) FK + MQ + KP + AM + QK + PF

To simplify this expression, we can group the vectors with similar directions and add them together. Let's rearrange the expression:

FK + KP + PF + MQ + QK + AM

Now, let's add the vectors with similar directions:

FK + KP + PF = (F + K + P)

MQ + QK = (M + Q)

AM = A

Therefore, the simplified expression for a) is (F + K + P) + (M + Q) + A.

b) AD + MP + EK - EP - MD

To simplify this expression, we can group the vectors with similar directions and add or subtract them accordingly. Let's rearrange the expression:

AD + MP + EK - EP - MD

Now, let's add or subtract the vectors with similar directions:

AD - MD = (A - M)

MP = M

EK - EP = (E - P)

Therefore, the simplified expression for b) is (A - M) + M + (E - P).

c) AC - BC - PM - AP + BM

To simplify this expression, we can group the vectors with similar directions and add or subtract them accordingly. Let's rearrange the expression:

AC - BC - PM - AP + BM

Now, let's add or subtract the vectors with similar directions:

AC - BC = (A - B)

PM = P

AP = (A - P)

Therefore, the simplified expression for c) is (A - B) - P + (A - P) + BM.

Please note that the simplified expressions are based on the assumption that the vectors are in the same coordinate system and can be added or subtracted accordingly.