Question

Дaно векторы A(4;-3;0) B(-6;0;8) Найдите |а|+|b|​

Answer 1

Ответ:

15

Пошаговое объяснение:

$|\vec{a}|=\sqrt{4^2+(-3)^2+0^2}= \sqrt{25} =5\\ \\ |\vec{b}|=\sqrt{(-6)^2+0^2+8^2} =\sqrt{100}=10 \\ \\ |\vec{a}|+|\vec{b}|=5+10=15$

Answer 2

To find the magnitude of vectors A and B and then calculate |A| + |B|, we use the formula for the magnitude (also known as the norm or length) of a vector:

For a 3D vector v = (x, y, z), the magnitude |v| is given by: |v| = sqrt(x^2 + y^2 + z^2)

Let's calculate the magnitudes of vectors A and B and then find their sum:

Vector A: A(4, -3, 0) |A| = sqrt(4^2 + (-3)^2 + 0^2) |A| = sqrt(16 + 9 + 0) |A| = sqrt(25) |A| = 5

Vector B: B(-6, 0, 8) |B| = sqrt((-6)^2 + 0^2 + 8^2) |B| = sqrt(36 + 0 + 64) |B| = sqrt(100) |B| = 10

Now, we can find |A| + |B|: |A| + |B| = 5 + 10 |A| + |B| = 15

Therefore, the result is |A| + |B| = 15.