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Given a vector (A1, A2, A3) and B vector (B1, B2, B3), then A1 / B1 = A2 / B2 = A3 / B3 is a sufficient condition of a vector / / b vector If a vector (A1, A2, A3) and B vector (B1, B2, B3) are known, then A1 / B1 = A2 / B2 = A3 / B3 is a sufficient and unnecessary B necessary C sufficient and necessary D of a vector / / b vector
A not necessary
If plane vector AI satisfies | AI | = 1 (I = 1, 2, 3) and vector AI * a (I + 1) = 0 (I = 1, 2, 3), then there are several possible values of | a1 + A2 + a3 + A4 |
A1, A2, A3 and A4 are unit vectors, and A1 is perpendicular to A2, A2 to A3 and A3 to A4
Because A2 is perpendicular to A3, A3 = A1 or A3 = - A1, and A3 is perpendicular to A4, then A4 = A2 or A4 = - A2
1) If A3 = A1 and A4 = A2, then: | a1 + A2 + a3 + A4 | = 2 | a1 + A2 | = 2sqrt (2)
2) If A3 = A1 and A4 = - A2, then: | a1 + A2 + a3 + A4 | = 2 | A1 | = 2
3) If A3 = - A1 and A4 = A2, then: | a1 + A2 + a3 + A4 | = 2 | A2 | = 2
4) If A3 = - A1 and A4 = - A2, then: | a1 + A2 + a3 + A4 | = 0
So there are three possible values of | a 1 + a 2 + a 3 + a 4
If the vertex coordinates of the triangle are (A1, B1), (A2, B2), (A3, B3), then the G coordinate of the center of gravity is? About the plane vector
G coordinate = ((a1 + A2 + a3) / 3, (B1 + B2 + B3) / 3, (C1 + C2 + C3) / 3)
How to orthogonalize vector group A1 = (1,1,1), A2 = (1,2,3), A3 = (1,4,9) by Schmidt method?
Solution:
b1=a1=(1,1,1)
b2=a2-(a2,b1)/(b1,b1)b1 = (1,2,3)-(6/3)(1,1,1)=(-1,0,1)
b3=a3-(a3,b2)/(b2,b2)b2-(a3,b1)/(b1,b1)b1
= (1,4,9)-(8/2)(-1,0,1)-(14/3)(1,1,1)
= (1/3,-2/3,1/3).
Please accept if you are satisfied^_^
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