Question

Для данных двух векторов a= -2i + j и b= 2i - 3j найдите длину вектора

Answer 1

1) |3b| = 3|b| = 3 $3 * \sqrt{2^{2} + (-3)^{2}} = 3\sqrt{13}$

2) |a - b| = |-4i + 4j| = $4\sqrt{2}$

3) 1/2 * |a - 4b| = 1/2 * |-10i + 13j| = $\frac{\sqrt{269}}{2}$

4) 1/2 * |-6a + b| = 1/2 * |14i - 9j| = $\frac{\sqrt{277}}{2}$

Answer 2

a(-2; 1), b(2; -3)

1) 3b = 3*(2; -3) = (6; -9)

|3b| = √(6² + (-9)²) = √(36 + 81) = √117 = 3√13

2) a - b = (-2 - 2; 1 - (-3)) = (-4; 4)

|a - b| = √((-4)² + 4²) = √32 = 4√2

3) 0,5a - 2b = 0,5*(-2; 1) - 2*(2; -3) = (-1; 0,5) - (4; -6) = (-1 - 4; 0,5 - (-6)) = (-5; 6,5)

|0,5a - 2b| = √(25 + 42,25) = √67,25

4) -3a + 0,5b = -3*(-2; 1) + 0,5*(2; -3) = (6; -3) + (1; -1,5) = (6 + 1; -3 - 1,5) = (7; -4,5)

|-3a + 0,5b| = √(49 + 20,25) = √69,25