pouydalpawan
Answered

At Westonci.ca, we provide clear, reliable answers to all your questions. Join our vibrant community and get the solutions you need. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform.

Find the area of the parallelogram determined by the vectors i +j+k and –2i + 3j + K.​

Sagot :

LammettHash

The area of the parallelogram spanned by the given vectors is equal to the magnitude of their cross product.

(i + j + k) × (-2i + 3j + k)

= -2 (i × i) - 2 (j × i) - 2 (k × i)

… + 3 (i × j) + 3 (j × j) + 3 (k × j)

… + (i × k) + (j × k) + (k × k)

= - 2 (j × i) - 2 (k × i) + 3 (i × j) + 3 (k × j) + (i × k) + (j × k)

= 2 (i × j) - 2 (k × i) + 3 (i × j) - 3 (j × k) - (k × i) + (j × k)

= 5 (i × j) - 3 (k × i) - 2 (j × k)

= 5 k - 3 j - 2 i

Then the area of the parallelogram is

||-2 i - 3 j + 5 k|| = √((-2)² + (-3)² + 5²) = √38

We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Keep exploring Westonci.ca for more insightful answers to your questions. We're here to help.