If e1, e2 are a set of bases representing all vectors in the plane, then the base (1) E1-e2 and 1/2e1+1/2e2(2)1/2e1-1/3e2 and 3e1-2e2(3) e1+1/3e2 and 3e1+e2

If e1, e2 are a set of bases representing all vectors in the plane, then the base (1) E1-e2 and 1/2e1+1/2e2(2)1/2e1-1/3e2 and 3e1-2e2(3) e1+1/3e2 and 3e1+e2

(3), Their direction vectors are the same.!

Of the following vectors, those that can be used as the base of the vector representing the plane in which they are located are Aa=(0,0), b=(2,1) Ba=(3,5) b=(-9,-15) Ca=(-1,2) b=(2,4) Da=(3,9) b=(1/9,1/3)

Non-zero vector and non-parallel, select c

The following statements are incorrect () A. Zero vector has no direction B. Zero vector parallel to any vector C. Zero vector length is zero D. Direction of zero vector is arbitrary The following statements are wrong () A. Zero vector has no direction B. Zero vector parallel to any vector C. Zero vector length is zero D. Direction of zero vector is arbitrary

According to the definition of zero vector: the vector with modulus of zero is zero vector to judge C pair
The direction of a zero vector is arbitrary; the zero vector is parallel to any vector
Judge B, D pair, judge A error
Guxuan A

The necessary and sufficient condition for vector a‖ vector b is the existence of a unique real number m, so that vector b=m vector a, no? Can you explain in more detail For example: m=0 or unequal 0 problem What is the condition of the former? The necessary and sufficient condition for vector a‖ vector b is the existence of a unique real number m, so that vector b=m vector a, no? Can you explain it in more detail? For example: m=0 or unequal 0 problem What is the condition of the former?

Excuse me.
To correct this, I just made a mistake in a place where a, b are all zero before m
(If a is not emphasized, b is not equal)
The latter is a sufficient and unnecessary condition for the former

A sufficient and necessary condition for any two vectors,(=),// in a space is that there is a real number λ, so that =λ Any two vectors a, b in space (b=0), a//b if and only if there is a real number λ so that a=λb Excuse me: why the sufficient and necessary condition can not be the existence of real number λ, so that b=λa Who doesn't know the necessary and sufficient conditions? Please take a careful look at the problem b is not equal to zero because b is not equal to zero, so in case a is zero vector b can not be expressed with a.

0

Given that A, B, C, P are four points in the plane, it is proved that A, B, C are on a straight line if and only if there is a pair of real numbers m, n such that vector PC=m It's been a long time. It's the process, There is a pair of real numbers m, n such that vector PC=m vector PA+n vector PB, and m+n=1" Given that A, B, C, P are four points in the plane, it is proved that A, B, C are on a straight line if and only if there is a pair of real numbers m, n such that vector PC = m ( It's been a long time. It's the process, There is a pair of real numbers m, n such that vector PC=m vector PA+n vector PB, and m+n=1"

Prove sufficiency: PC = mPA + nPB = m (PC + CA)+ n (PC + CB)=(m + n) PC + mCA + nCB = PC + mCA + nCB has mCA =- nCB, Necessity of re-verification: Since A, B and C are collinear, we can get AC=tAB, then PC=P...