Product Of Two Vectors

To find the value of in the expression , we start with the given vectors:

Using the vector triple product identity, we have:

Plugging in the given expression, we need:

From the equation above, we equate coefficients:

This implies:

Next, calculate :

Thus, . Plugging this into the equation:

Therefore, the value of is .

The correct answer is .

We are given:

Step 1: Properties of the vectors

1. The dot product: This implies that and are perpendicular.
2. The cross product:

Step 2: Relationship involving angle

Let be the angle between and . The magnitude of their product is:

The magnitude of the dot product is:

Step 3: Solve for

Divide the equations to find :

Step 4: Find

From the given relationships:

Step 5: Find

From the magnitude relationship:

Final Answer: