Word Count : 406

---

To find the transformation of the given equation under the given rotation of axes while keeping the origin fixed, follow these steps: ### Given equation: \[ 12x^2 - 2y^2 + z^2 = 2xy \] ### Given direction cosines: The new coordinate axes have direction ratios as: - New \( x' \)-axis: \( (1, -3, 0) \) - New \( y' \)-axis: \( (3, 1, 0) \) - New \( z' \)-axis: \( (0, 0, 1) \) #### Step 1: Construct the ___ _______ _______ ________ _______ _____ ____ _______.
__________ ________ ___ _________ _________ _____ ______ _____.
__________ ___ ______ ______ _____ ____ ___ ______.
_________ _________ _________ ________ _________ ______ ___.
___ ___ _________ _______ _____.
___ ____ ___ _______ ________ ________ ______ ________ ______ ______.
______ ____ ___ ____ ___ ____.
___ ___ ___ _______ _____.
___ ___ _______ ____ _________ ___ ____ __________ ___ ___ ____ ____.
______ _________ ___ ____ _______ _______.
______ _________ _____ ____ ____ ____ _____ ______ _______ ____ _____.
________ _______ ________ _________ ______ ______ _______ _________ ___ ________.
_____ ___ ______ _________ _________ ___ ____ _______ __________.
_________ ________ ______ ________ ______ ___ _________ ________ ___ _______ _______ _______.
_____ _________ _________ ___ _____ _______.
_________ _________ ____ _____ __________ _________ ______ ____ _____.
_____ _________ _____ _____ ___ ______ _________.
____ _________ ______ __________ __________.
________ ____ _______ ____ ___ __________ _______ ________ ______.
___ _________ ___ _______ _____ __________ _________ _________ _____.
_________ ______ _______ ____ _______.
________ __________ ______ __________ _____ _______.
_______ ____ _______ _____ _________ _______ ________ _____ _______ ________ _____.
________ ______ ________ _______ ___ _________ ____ __________ __________ ______ _______.
___ ____ ______ ____ ________ ___ ________.
__________ _________ _______ __________ ___.
_________ ___ _________ _________ ________ _______ ___ ___ ____.
_________ ____ _____ ________ _______ __________ ________ ____ ______ _________ ___.
___ __________ _______ ___ _________ _______.
___ ___ ____ ______ _______ ______ __________ _______ _________.
__________ ____ _______ _____ _________ _____ _______ _____ __________ _____.
____ _____ ________ _____ _____ _______ _______.
________ _________ ____ __________ ________ _____ __________ _______ _______ ____ ___ ________.
_________ ______ _______ ________ ___ _________ ____ ___ ________ ________.
__________ _______ ___ _______ _____ _______ __________.
______ ______ _________ _______ ________ ________ ____ __________ ______ ____ __________.
______ ___ ________ _______ ________ _______ _______ _______ _____ ____.
_______ ____ ______ ___ ________ ________ ______ ___ ________ __________.
______ _____ _____ ____ ____.
_______.
Get Full Answer on WhatsApp