Question

已知向量a=(-3,4)向量a平行b，且丨b丨=1，则b=

过程谢谢

Answer 1

let b=(x,y)
a//b
-3/4 = x/y
x = (-3/4)y
|b|^2=1
x^2 +y^2 =1
(9/16)y^2 +y^2 =1
y^2 = 16/25
y = 4/5 or -4/5
b=(-3/5, 4/5) or (3/5,-4/5)

Answer 2

向量a平行b，则有：a=tb
丨b丨=1
所以有：
(-3t)^2+(4t)^2=1
解得：t=1/5 或 t=-1/5
当t=1/5时有：b(-3/5,4/5)
当t=-1/5时有：b(3/5,-4/5)