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Known vector OA=(k,12), OB=(4,5), OC=(-k,10), and A, B and C are collinear, then the value of k is () A.-2 3 B.4 3 C.1 2 D.1 3
AB =
OB−
OA=(4−k,−7);
AC =
OC−
OA=(−2k,−2)
A, B and C are collinear
∴
AB,
AC collinear
-2×(4-K)=-7×(-2k)
Solution k=−2
3
Therefore, A.
Three vectors are known OA=(k,12), OB=(4,5), OC=(10, k), and A, B and C are collinear, then k=______.
From the meaning
AB=(4-k,-7),
BC =(6, k-5) due to
AB and
BC collinear,
So (4-k)(k-5)+42=0, k=11 or k=-2.
Therefore, the answer is:-2 or 11.
From the meaning of the title
AB=(4-k,-7),
BC =(6, k-5) due to
AB and
BC collinear,
So (4-k)(k-5)+42=0, k=11 or k=-2.
Therefore, the answer is:-2 or 11.
Proving that three vectors are coplanar
Vector k1a-k2b+(k2b-k3c)=k1a-k3c=-(k3c-k1a),
The vectors k1a-k2b, k2b-k3c, k3c-k1a are coplanar.
How to prove vector coplanar
Let a, b, c be three vectors. Let a, b, c be coplanar if the mixed product of a, b, c is 0.
Or one of the proofs may be represented by two other linear numbers, for example, the proofs have real numbers x, y such that a=x·b+y·c
There are several methods to prove that space vectors are coplanar What else but finding the sum of constants as one?
Mixed product is 0;
Their 3rd order determinant is 0;
Find the real numbers a, b, c which are not all 0 such that ax + by + cz x, y, z are vectors;
The normal vectors of any two of their defined planes are parallel
Mixed product is 0;
The third order determinant is 0;
Find the real numbers a, b, c which are not all 0 such that ax + by + cz x, y, z are vectors;
The normal vectors of any two of their defined planes are parallel
Mixed product is 0;
Their third order determinant is 0;
Find the real numbers a, b, c which are not all 0 such that ax + by + cz x, y, z are vectors;
The normal vectors of any two of their defined planes are parallel
How to Prove Four-Point Coplanar (Knowledge Using Space Vector) How to Prove Four-Point Coplanar (the knowledge of space vector)
Take any two points as the vector, take the other two points as the vector, prove that the two vectors are parallel or intersect.
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