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Given a (-1,2,3), vector b (1,1,1), the module of the projection of vector a in the direction of vector b is
According to the meaning, cosine value of angle between two vectors cosθ=-1+2+3/√14 3=4/√42
The module of the projective vector a in the direction of vector b=√14*cosΘ=√14*4/√42=4√3/3,
Given the direction vector e=(-4/5,3/5) of the straight line L on the plane, the projectiles of points A (-1,1) and B (0,-1) on L are A1, B1, respectively. If vector A1B1= lambda vector e, then the value of lambda is
Vector AB=(1,-2)
According to the projective formula |A1B1|=|AB|cosa=AB*e/|e|
|A1B1|=AB*e/|e|=-4/5*1-3/5*2
=-2
Because |e|=1
Therefore, the value of λ is -2
In the space rectangular coordinate system, O-xyz, point B is the orthographic projection of point A (1,2,3) in the coordinate plane yOz, then OB is equal to ______. In the space rectangular coordinate system, O-xyz, point B is the positive projective of point A (1,2,3) in the coordinate plane yOz, then OB is equal to ______.
Point B is the positive projection of point A (1,2,3) in the coordinate plane yOz,
B On the coordinate plane yOz, the vertical and vertical marks are the same as A, while the horizontal mark is 0,
The coordinates of B are (0,2,3),
OB equals
22+32=
13,
Therefore, the answer is:
13.
In the plane rectangular coordinate system xoy, if a (-3,1), b (3,4) is known, then the projection of vector oa in the vector ob direction is In the plane rectangular coordinate system xoy, given a (-3,1), b (3,4), the projection of vector oa in the vector ob direction is
Recommendation: Do not write the projection of a in direction b directly
Don't write the projection of OA in OB direction, and do n' t mix case:
A·b=(-3,1)·(3,4)=-9+4=-5
|B|=5, so the projection of a in direction b:
|A|cos=a·b/|b|=-5/5=-1
------------------------- Or: point A (-3,1), point B (3,4)
OA·OB=(-3,1)·(3,4)=-9+4=-5
|OB|=5, so the projection of OA in OB direction:
|OA|cos=OA·OB/|OB|=-5/5=-1
In the rectangular coordinate plane, vector OA=(4,1), vector OB=(2-3), the two vectors have the same orthographic length on the straight line L, then what is the slope of L
Let a reference vector OC=(1, k)
Calculate the projection of OA and OB on OC respectively, because the projection has positive and negative, the problem only requires the same length, so add an absolute value.
(4*1+1*K)/k square under root sign +1=(2*1-3*k)/k square under root sign +1
(4*1+1*K)/k square under root sign +1=-(2*1-3*k)/k square under root sign +1
Find k=3 and k=-1/2
Is the projection of vector a in vector b a quantity or a vector Is the projection of vector a in the direction of vector b a number or a vector
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