The Formula of Vertical Vector b of Vector a

The Formula of Vertical Vector b of Vector a

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Known A =(2,-1,3), B=(-1,4,-2), C=(7,7,λ), if A. B. If c is a three-vector coplanar, then the real number λ is equal to () A.3 B.5 C.7 D.9

∵

A.

B.

C Three-vector coplanar,
∴

C=x

A+y

B, x, y∈R,
(7,7,λ)=(2X,-x,+3x)+(-y,4y,-2y)=(2x-y,-x+4y,3x-2y),
2X-y=7,-x+4y=7,3x-2y=λ,
λ=9;
Therefore, D.

Given vector a=(1,2), vector b=(x,-1), and a⊥b, then the real number x is equal to A,-4 B,4 C,-2 D,2 Given vector a=(1,2), vector b=(x,-1), and a⊥b, then the real number x equals A,-4 B,4 C,-2 D,2

Select D

Given two vectors a=(3,4), b=(2,-1), and (a+xb)⊥(a-b), then the real number x is equal to ()

A+xb=(3+2x,4-x) a-b=(1,5)
(A+xb)⊥(a-b),
(A+xb)*(a-b)
=(3+2X,4-x)(1,5)
=3+2X+20-5x
=23-3 X =0
X =23/3

Given vector a=(2,-1,3), b (-1,4,-2), C=(7,5, in), if three vectors a, b, c are coplanar, then the real number in is equal to

Vector a=(2,-1,3), b (-1,4,-2), C=(7,5, in), if the three vectors a, b, c are coplanar have real numbers m, n, such that c=ma+nb (7,5, in)=m (2,-1,3)+n (-1,4,-2)7=2m-n15=-m+4n2=3m-2n31+2*2 17=7n n=17/7 m=33/7 in=3m-...

Given a=(2,-1,3), b=(-1,4,-2), c=(7,-7,11), if the vector a=λ(b+c) coplanar, then the real number λ equals

λ=1/3.
The vector a=λ(b+c) can be obtained by making the corresponding coordinates equal.