What is the resultant of unit vector s ` hatj and hatk` ?
[ Hint : ` |hatj| = |hatk| =1`]

Answer

To find the resultant of the unit vectors \( \hat{j} \) and \( \hat{k} \), we can follow these steps:

### Step 1: Identify the Vectors
We have two unit vectors:
- \( \hat{j} \) (which represents the unit vector in the y-direction)
- \( \hat{k} \) (which represents the unit vector in the z-direction)

### Step 2: Write the Resultant Vector
The resultant vector \( \vec{R} \) can be expressed as the sum of the two vectors:
\[ \vec{R} = \hat{j} + \hat{k} \]

### Step 3: Calculate the Magnitude of the Resultant Vector
To find the magnitude of the resultant vector, we use the Pythagorean theorem. The magnitude \( |\vec{R}| \) is given by:
\[ |\vec{R}| = \sqrt{(\text{coefficient of } \hat{j})^2 + (\text{coefficient of } \hat{k})^2} \]
Since both coefficients are 1 (because \( \hat{j} \) and \( \hat{k} \) are unit vectors):
\[ |\vec{R}| = \sqrt{1^2 + 1^2} = \sqrt{1 + 1} = \sqrt{2} \]

### Step 4: Write the Resultant in Vector Form
Thus, the resultant vector can be expressed as:
\[ \vec{R} = \hat{j} + \hat{k} \]
And its magnitude is:
\[ |\vec{R}| = \sqrt{2} \]

### Final Answer
The resultant of the unit vectors \( \hat{j} \) and \( \hat{k} \) is:
\[ \vec{R} = \hat{j} + \hat{k} \quad \text{with magnitude } |\vec{R}| = \sqrt{2} \]

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