Given the vector OA=(3,-4) OB=(6,-3) OC=(5-m,-3-m)(1) If AB C is three points collinear, then the value of m Given the vector OA=(3,-4) OB=(6,-3) OC=(5-m,-3-m)(1) If AB C is three points collinear, the value of the number m

Given the vector OA=(3,-4) OB=(6,-3) OC=(5-m,-3-m)(1) If AB C is three points collinear, then the value of m Given the vector OA=(3,-4) OB=(6,-3) OC=(5-m,-3-m)(1) If AB C is three points collinear, the value of the number m

Three-point collinear;
AB//AC
AB=OB-OA=(3,1)
AC=OC-OA=(2-m,1-m)
3/(2-M)=1/(1-m);
3-3M =2-m;
2 M =1;
M=1/2;
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If vector a is multiplied by vector b is equal to 0, then vector a is equal to 0, or vector b is equal to 0. True or false proposition. If vector vector a is multiplied by the vector b is equal to 0, then the vector a is equal to 0, or the vector b is equal to 0. True or false.

A:
False propositions, it is possible that the vectors a, b are not 0, then they are vertical.

A:
False propositions, it is possible that the vectors a, b are not 0 and they are vertical.

Vector a=(3,4) is known, vector b is opposite to direction a, and vector b in |a|=15. is equal to?

Should be |b|=15,|a|=5.
-A =(-3,-4),|a|=√(3^2+4^2)=5
So b=-a*(15/5)=(-9,-12)

In triangle ABC, it is known that 2*vector AB*vector AC = root number 3*Ivector ABI*Ivector ACI = square of 3vector BC, and the magnitude [II is absolute value Thank you In triangle ABC, it is known that 2*vector AB*vector AC = root number 3*Ivector ABI*Ivector ACI = square of 3vector BC, and the magnitude of angle ABC [II is the absolute value Thank you

2A B*AC=√3|AB AC| AB*AC/(|AB AC|)=√3/2, i.e. cosA=√3/2, then angle A=π/6, so C+B=5π/6 and √3|AB AC|=3|BC|2|AB AC|=√3|BC|2 is a sine theorem with...

2A B*AC=√3|AB AC| AB*AC/(|AB AC|)=√3/2, i.e., cosA=√3/2, then angle A=π/6, so C+B=5π/6 and √3|AB AC|=3|BC|2 AB AC|=√3|BC|2 is a sine theorem with...

Given vector a=(-1,1), b=(3, m), a‖(a+b), then m=?

A + b =(2, m +1)
A//(a+b)
-1/2=1/(M+1)
-M-1=2
M=-3

Given a vector =(2,3), b =(-1,2), if ma+nb is collinear with a-2b, then m/n equals

Ma+nb=(2m-n,3m+2n)
A-2b=(4,-1)
Because they're collinear.
So (2m-n)/4=(3m+2n)/(-1)
As a result:
M/n = negative half