`bar(r)=2bar(i)+3bar(j)-6bar(k)" then find "abs(bar(r))`.

Answer

To find the modulus of the vector \(\bar{r} = 2\bar{i} + 3\bar{j} - 6\bar{k}\), we can follow these steps:

### Step 1: Identify the components of the vector
The vector \(\bar{r}\) can be expressed in terms of its components:
- \(x = 2\) (coefficient of \(\bar{i}\))
- \(y = 3\) (coefficient of \(\bar{j}\))
- \(z = -6\) (coefficient of \(\bar{k}\))

### Step 2: Write the formula for the modulus of a vector
The modulus (or magnitude) of a vector \(\bar{r} = x\bar{i} + y\bar{j} + z\bar{k}\) is given by the formula:
\[ |\bar{r}| = \sqrt{x^2 + y^2 + z^2} \]

### Step 3: Substitute the values of \(x\), \(y\), and \(z\)
Substituting the values we identified:
\[ |\bar{r}| = \sqrt{(2)^2 + (3)^2 + (-6)^2} \]

### Step 4: Calculate the squares of the components
Calculating each term:
- \(2^2 = 4\)
- \(3^2 = 9\)
- \((-6)^2 = 36\)

### Step 5: Add the squared values
Now, add these squared values together:
\[ |\bar{r}| = \sqrt{4 + 9 + 36} \]
\[ |\bar{r}| = \sqrt{49} \]

### Step 6: Calculate the square root
Finally, calculate the square root:
\[ |\bar{r}| = 7 \]

Thus, the modulus of the vector \(\bar{r}\) is \(7\).

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