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Suppose = (-3, 3) and = (-12, 0) are two vectors that form the sides of a parallelogram. Then the lengths of the two diagonals of the parallelogram are Separate answers with a comma.

Suppose = (-3, 3) and = (-12, 0) are two vectors that form the sides of a parallelogram. Then the lengths of the two diagonals of the parallelogram are Separate answers with a comma.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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MAA MATHEMATICAL ASSOCIATION OF AMERICA Previous Problem Problem List Next Problem 201-114-A04: Problem 12 (1 point) Suppose = (-3, 3) and = (-12, 0) are two vectors that form the sides of a parallelogram. Then the lengths of the two diagonals of the parallelogram are Separate answers with a comma. Preview My Answers Submit Answers You have attempted this problem 0 times. You have unlimited attempts remaining. Email Instructor
Transcribed Image Text:MAA MATHEMATICAL ASSOCIATION OF AMERICA Previous Problem Problem List Next Problem 201-114-A04: Problem 12 (1 point) Suppose = (-3, 3) and = (-12, 0) are two vectors that form the sides of a parallelogram. Then the lengths of the two diagonals of the parallelogram are Separate answers with a comma. Preview My Answers Submit Answers You have attempted this problem 0 times. You have unlimited attempts remaining. Email Instructor
Expert Solution
Step 1

The sum of the vectors 

u + v = (-3, 3) + (-12, 0)u + v = (-15, 3)

The points to the vertex of the parallelogram are opposite to the origin.

Its distance from the origin is the length of one of the diagonals:

So,

||(-15, 3)|| = (-15)2+ (3)2 = 225 + 9 = 234So, ||(-15, 3)|| = 326

So, length of one diagonal is 326 units 

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