Vectors

We have,

Step 1: Use given magnitudes to find .
Given , so Thus . Step 2: Express in terms of .
We know . Hence So Step 3: and the final expression.
From we get Thus Hence Finally, Therefore, is the value of .

A plane perpendicular to two given planes will have its normal vector parallel to the cross product of the normal vectors of the given planes.

The normal to the plane is:

The normal to the plane is:

Expanding the determinant:

Since the normal to the required plane is parallel to , we take:

Thus,

Since normal vectors can be scaled, dividing by 9, we get:

Thus, the correct answer is .

N/A

Step 1: A vector perpendicular to the plane of .<
A suitable vector is parallel to . First find Compute: So Step 2: Let be a scalar multiple.
Thus Step 3: Projection on .
The magnitude of the projection of onto is We’re given this is . Now So Next, Hence: We can assume if direction is not specifically reversed. So . Step 4: .
Hence Therefore .