Question

Даны векторы а(-2;3;0), b(1;3;1), с(0;5;-4)найти вектор p=a+3b-2c

Answer 1

3b = (3;9;3) 2c = (0;10;-8)

p = (-2;3;0) + (3;9;3) - (0;10;-8) = (1;2;11)

Answer 2

To find the vector p, which is equal to a + 3b - 2c, we need to perform vector addition and scalar multiplication. Let's go step by step:

Given vectors: a = (-2, 3, 0) b = (1, 3, 1) c = (0, 5, -4)

Step 1: Perform scalar multiplication.

• 3b = 3 * (1, 3, 1) = (3, 9, 3)
• 2c = 2 * (0, 5, -4) = (0, 10, -8)

Step 2: Perform vector addition. a + 3b - 2c = (-2, 3, 0) + (3, 9, 3) - (0, 10, -8)

Step 3: Add the corresponding components. p = (a_x + 3b_x - 2c_x, a_y + 3b_y - 2c_y, a_z + 3b_z - 2c_z) p = (-2 + 3 - 0, 3 + 9 - 10, 0 + 3 + 8)

Step 4: Simplify. p = (1, 2, 11)

So, the vector p is (1, 2, 11).