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It is known that E1 and E2 are a set of bases of plane vectors, and a = E1 + E2, B = 3e1-2e1, C = 2E1 + 3e2 If C = a + UB (where u belongs to R), try to find the sum U
2 = input + 3U
3 = in-2u
So, in = 7 / 5, u = - 1 / 5
It is known that E1 and E2 are the bases of a set of plane vectors. If Ke1 + E2 and 12e1 + TE2 are collinear, all the positive integers K and t satisfying the condition are obtained
kt＝12,（k,t）∈｛（1,12）,（2,6）,（3,4）,（4,3）,（6,2）,（12,1）｝
(1) Known: plane vector a (2,3): find the coordinates of a with E1 (2,0) E2 (0,2) vector as the base
(1) Known: plane vector a (2,3)
Find: the coordinate of a based on E1 (2,0) E2 (0,2) vector
a=x1e1+x2e2
(2,3)=(2,0)x1+(0,2)x2
2=2x1+0
x1=1
3=0×x1+2x2
x2=3/2
therefore
The coordinates are (1,3 / 2)
It is known that E1 and E2 are non collinear vectors, a = 3e1-4e2, B = (1-N) e1 + 3ne2. If a / / B, then the value of n is?
I'm good at this,
a=3e1-4e2=(3,-4),b=(1-n)e1+3ne2=(1-n,3n),
A / / B, then 3 * 3N + 4 * (1-N) = 0,
So, n = - 4 / 5
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