Define a set of (non-orthogonal) base vectors a = J + K, + K and c 1+J. q = i +4j and r = − (a) Establish their reciprocal vectors and hence express the vectors p = 3i—2j+k, -2i+j+ k in terms of the base vectors a, b and c. (b) Verify that the scalar product p q has the same value, −5, when evaluated using either set of components.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Define a set of (non-orthogonal) base vectors a =j+k, b = i + k and c = i + j.
(a) Establish their reciprocal vectors and hence express the vectors p = 3i—2j+k,
q = i +4j and r = −2i+j+ k in terms of the base vectors a, b and c.
(b) Verify that the scalar product p q has the same value, -5, when evaluated
using either set of components.
Transcribed Image Text:7.25 Define a set of (non-orthogonal) base vectors a =j+k, b = i + k and c = i + j. (a) Establish their reciprocal vectors and hence express the vectors p = 3i—2j+k, q = i +4j and r = −2i+j+ k in terms of the base vectors a, b and c. (b) Verify that the scalar product p q has the same value, -5, when evaluated using either set of components.
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