1. Let ā=ī-2j+k, b = i +4j-5k, c = 5i + j - 2k & d = -2ī-j+k. Answer each of the following: Sketch each of the above vectors in a rectangular coordinate system for R³. Find the vector 3ā - 2(b + c)-d. Determine if the vector (a + b) is orthogonal to the vector (c- d); If not, find the cosine of the angle between them. (iv) If P = (3,-1,3), Q = (1,-5,5), and R = (2,2,3), determine if the vector PQ is parallel to the vector ā. Find the (i) Compā; (ii)Projā; (i) € (iii) (v)
1. Let ā=ī-2j+k, b = i +4j-5k, c = 5i + j - 2k & d = -2ī-j+k. Answer each of the following: Sketch each of the above vectors in a rectangular coordinate system for R³. Find the vector 3ā - 2(b + c)-d. Determine if the vector (a + b) is orthogonal to the vector (c- d); If not, find the cosine of the angle between them. (iv) If P = (3,-1,3), Q = (1,-5,5), and R = (2,2,3), determine if the vector PQ is parallel to the vector ā. Find the (i) Compā; (ii)Projā; (i) € (iii) (v)
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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Plz answer part 1,3 and 4 correctly asap
Transcribed Image Text:Question:
1. Let ā=ī-2j+ k, b=-i +4j-5k, c = 5i +j-2k&d=-2ī-j+ k. Answer
each of the following:
(1) Sketch each of the above vectors in a rectangular coordinate system for
R³.
Find the vector 3ā - 2(b + c)-d.
Determine if the vector (a + b) is orthogonal to the vector (- d); If not,
find the cosine of the angle between them.
(iv)
If P = (3,-1,3), Q = (1,-5,5), and R = (2,2,3), determine if the vector
PQ is parallel to the vector ā.
Find the (i) Compa; (ii)Projā;
(iii)
(v)
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