Question

Будут ли векторы a и b коллинеарными, если: a=(-2;1), b=(4;-2)? (с решением, плиз)

Answer 1

Решение смотри на фотографии

Answer 2

Checking for Collinearity of Vectors

To determine if vectors a and b are collinear, we can check if one is a scalar multiple of the other. In other words, if one vector is a multiple of the other, they are collinear.

The condition for collinearity is that if a and b are collinear, then b = ka for some scalar k.

Solution

Given vectors a = (-2, 1) and b = (4, -2), we can check if b is a scalar multiple of a.

We can calculate the scalar k by dividing the corresponding components of b by the corresponding components of a.

The scalar k can be calculated as follows: - For the x-component: k = 4 / (-2) = -2 - For the y-component: k = (-2) / 1 = -2

Since both components of b are scalar multiples of the corresponding components of a with k = -2, a and b are collinear.

Therefore, the vectors a and b are collinear.

Conclusion

The vectors a = (-2, 1) and b = (4, -2) are collinear, as b is a scalar multiple of a with k = -2.