Write the value of `(hatk X hatj).(hati+hatj+hatk)`

Answer

To solve the problem `(hatk × hatj) · (hati + hatj + hatk)`, we will follow these steps:

### Step 1: Identify the Cross Product
We need to compute the cross product `hatk × hatj`. According to the right-hand rule and the properties of the unit vectors:
- `hatk × hatj = -hati`

### Step 2: Substitute the Cross Product into the Dot Product
Now we substitute `hatk × hatj` into the expression:
- `(hatk × hatj) · (hati + hatj + hatk) = (-hati) · (hati + hatj + hatk)`

### Step 3: Distribute the Dot Product
Next, we will distribute the dot product:
- `(-hati) · (hati + hatj + hatk) = (-hati · hati) + (-hati · hatj) + (-hati · hatk)`

### Step 4: Calculate Each Dot Product
Now we calculate each of the dot products using the properties of unit vectors:
- `hati · hati = 1`
- `hati · hatj = 0`
- `hati · hatk = 0`

Substituting these values into our equation gives:
- `= -1 + 0 + 0`

### Step 5: Combine the Results
Finally, we combine the results:
- `-1 + 0 + 0 = -1`

### Final Answer
Thus, the value of `(hatk × hatj) · (hati + hatj + hatk)` is **-1**.

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