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Given point O (0,0) A (1,2) B (4,5) and vector OP=vector OA+t multiple vector (1) When t is, the point P is on the x-axis (2) Can the AB quadrilateral OABP become a parallelogram? If yes, find the value of t; if no, explain the reason Given point O (0,0) A (1,2) B (4,5) and vector OP=vector OA+t multiple vector (1) When t is, the point P is on the x-axis (2) Can the AB quadrilateral OABP become a parallelogram? If yes, find the value of t, if no, explain the reason
OP=OA+tAB, i.e. OP=(1,2)+t (3,3)=(3t+1,3t+2)(1) P is on the x axis, i.e.3t+2=0(2) parallelogram OABP is equivalent to OA+OP=OB, i.e.(1,2)+(3t+1,3t+2)=(4,5) t, so it can not be quadrilateral or AP=OP-OA=tAB=(3t,3t) AB=(4,5)-(1,2)=(3,3) vector AP parallel vector A.
Given O (0,0), A (1,2) B (4,5) and vector OP=vector OA+vector tAB 1. When t is the value, P is on the X axis, P is on the Y axis, and P is in the second quadrant. 2. Can quadrilateral OABP become parallelogram? If yes, find the corresponding value of t; if no, explain the reason
Vector OA=(1,2) Vector AB=(3,3)
So vector OP=(1+3t,2+3t)
P is on the X axis, then 2+3t=0, so t=-2/3
On the y-axis, then 1+3t=0, so t=-1/3
Second quadrant, then 1+3t0, so -2/3
Given two vectors A =(3,4), B=(2,1), if ( A+x B)⊥( A- B), the value of x equals ______.
∵
A =(3,4),
B=(2,1),
A2=9+16=25, b2=4+1=5
∵(
A+x
B)⊥(
A-
B) a2-xb2=25-5 x =0
X=5
Therefore, the answer is:5
Given vectors a=(1,2), b=(-3,0), if (2a+b)//(a-mb), then m=?
2A+b=(2*1-3,2*2+0)=(-1,4) a-mb=(1+m*3,2-m*0)=(3m+1,2) Parallel description corresponding to proportional coordinates,4/2=2=-1/(3m+1) So 6m+2=-1, m=-1/2. Please adopt the answer in the lower right corner in time,
2A+b=(2*1-3,2*2+0)=(-1,4) a-mb=(1+m*3,2-m*0)=(3m+1,2) corresponding to proportional coordinates,4/2=2=-1/(3m+1) So 6m+2=-1, m=-1/2. Please adopt the answer in the lower right corner in time,
Given three vectors a=(3,2), b=(-1,2), c=(4,1) in the plane, answer the following question (1), find the real number m satisfying a=mb+nc, n (2) if Give three vectors in the plane a=(3,2), b=(-1,2), c=(4,1). Answer the following questions (1) Find the real number m, n satisfying a=mb+nc (2) If (a+kc)‖(2b-a), the number k; (3) If d. satisfies (d-c)‖(a+b) and |d-c|=√5, find d.
(1) According to a=mb+nc,2=2m+n6=2m+8n, m=8/9, n=5/9(2) according to (a+kc)‖(2b-a),(3+4k,2+k) is parallel to (-5,2), then 3+4k/2+k=-5/2, k=10/13.(3)(d-c) is parallel to (a+b). Let d=(x.y) then (4-x)/(1-y)=(3-1)/(2+2)=1/2...
Given a parallel vector a, b satisfies |a|=1,|b|=2, the angle between a and b is 60°, then "m=1" is "(a-mb)⊥a" A. Sufficient and unnecessary conditions B. Necessary and insufficient conditions C. Sufficient and necessary conditions D. Inadequate and unnecessary conditions Given a parallel vector a, b satisfies |a|=1,|b|=2, the angle between a and b is 60°, then "m=1" is "(a-mb)⊥a" A. sufficient and unnecessary conditions B. necessary and insufficient conditions C. sufficient and necessary conditions D. neither sufficient nor necessary conditions Given that the parallel vectors a, b satisfy |a|=1,|b|=2, the angle between a and b is 60°, then "m=1" is "(a-mb)⊥a" A. Sufficient and unnecessary conditions B. Necessary and insufficient conditions C. Sufficient and necessary conditions D. Inadequate and unnecessary conditions
Ab ==1
When 1-m=0, a is perpendicular to b, m=1
The other way around.
C Necessary and Sufficient Conditions
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