Question 1 (30 Marks) (a) Given vectors P=5i+2j-4k and Q=2i-3j+5k . Evaluate the following (i) (5P+2Q)-(2P-3Q) (ii) Determine the magnitude of (3P+2Q)-(2P-3Q)

Question

Answer 1

(i) To evaluate

, we first need to find the expressions for

and

.

= 25i + 10j - 20k + 4i - 6j + 10k

= 29i + 4j - 10k

2P-3Q = 2(5i+2j-4k) - 3(2i-3j+5k)

= 10i + 4j - 8k - 6i + 9j - 15k

= 4i + 13j - 23k

(5P+2Q)-(2P-3Q)

(5P+2Q)-(2P-3Q) = (29i + 4j - 10k) - (4i + 13j - 23k)

= 29i + 4j - 10k - 4i - 13j + 23k

= 25i - 9j + 13k

(3P+2Q)-(2P-3Q)

(3P+2Q)-(2P-3Q) = 3(5i+2j-4k) + 2(2i-3j+5k) - (4i + 13j - 23k)

= 15i + 6j - 12k + 4i - 6j + 10k - 4i - 13j + 23k

= 15 6j - 12k + 4i - 6j + 10k - 4i - 13j + 23k

= 15i + 6j - 12k + 4i - 6j + 10k - 4i - 13j + 23k

= 15i + 6j - 12k + 4i - 6j + 10k - 4i - 13j +

= 15i + 6j - 12k + 4i - 6j + 10k - 4i - 13j + 23k

= 15i + 6j - 12k + 4i - 6j + 10k - 4i - 13

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