Question

A(-3;2;1) B(2;-1;-3) C(1;-4;3) D (-1;2;-2)—>. –>2AB+3CD​

Answer 1

Ответ:

Объяснение:

1)A(-3;2;1) B(2;-1;-3) тогда вектор АВ(2+3;-1-2;-3-1) , АВ(5;-3-4)  ,

2АВ(5*2;-3*2;-4*2)  ,  2АВ(10;-6;-8)

2)C(1;-4;3) D (-1;2;-2) , тогда СD(-1-1;2+4;-2-3)  , СD(-2;6;-5) , 3СD(-6;18;-15).

3) —>. –>

2AB+3CD​ (10-6;-6+18;-8-15)  ,

—>. –>

2AB+3CD​ (4;12;-23)

Answer 2

To find the vector 2AB + 3CD, we first need to calculate the vectors AB and CD, and then perform the scalar multiplication and vector addition.

The vector AB is the displacement from point A to point B, and it can be calculated as:

AB = B - A

Similarly, the vector CD is the displacement from point C to point D:

CD = D - C

Let's calculate AB and CD:

AB = (2, -1, -3) - (-3, 2, 1) AB = (2 + 3, -1 - 2, -3 - 1) AB = (5, -3, -4)

CD = (-1, 2, -2) - (1, -4, 3) CD = (-1 - 1, 2 + 4, -2 - 3) CD = (-2, 6, -5)

Now, we can perform the scalar multiplication and vector addition:

2AB = 2 * (5, -3, -4) = (2 * 5, 2 * -3, 2 * -4) = (10, -6, -8)

3CD = 3 * (-2, 6, -5) = (3 * -2, 3 * 6, 3 * -5) = (-6, 18, -15)

Finally, we can find the sum of 2AB and 3CD:

2AB + 3CD = (10, -6, -8) + (-6, 18, -15)

Adding the corresponding components:

= (10 - 6, -6 + 18, -8 - 15)

= (4, 12, -23)

So, the vector 2AB + 3CD is (4, 12, -23).