The (x,y,z) co -ordinates of two points A and B are give respectively as (0,3,- 1) and (-2,6,4) The displacement vector from A to B is given by

Options

A. `-2 hati+6hatj+4hatk`
B. `-2hati+3hatj+3hatk`
C. `-2hati+3hatj+5hatk`
D. `2hati-3hatj-5hatk`

Explanation

To find the displacement vector from point A to point B given their coordinates, we can follow these steps:

### Step 1: Identify the coordinates of points A and B
- Point A has coordinates \( A(0, 3, -1) \)
- Point B has coordinates \( B(-2, 6, 4) \)

### Step 2: Write the formula for the displacement vector
The displacement vector \( \vec{AB} \) from point A to point B can be calculated using the formula:
\[ \vec{AB} = \vec{B} - \vec{A} \]
This means we subtract the coordinates of point A from the coordinates of point B.

### Step 3: Perform the subtraction for each coordinate
Now, we will subtract the coordinates of A from B:
- For the x-coordinate:
\[ x_B - x_A = -2 - 0 = -2 \]
- For the y-coordinate:
\[ y_B - y_A = 6 - 3 = 3 \]
- For the z-coordinate:
\[ z_B - z_A = 4 - (-1) = 4 + 1 = 5 \]

### Step 4: Write the displacement vector
Now we can write the displacement vector \( \vec{AB} \):
\[ \vec{AB} = (-2, 3, 5) \]

### Final Answer
The displacement vector from point A to point B is:
\[ \vec{AB} = (-2, 3, 5) \]