Question

1. The vectors a, b and c are given by: a = 2î +3j - 4k b = 5î+4ĵ+ 7k c = 6i +2j-k Find: (i) 2a+3b-c (ii) a-2b+4c (iii) 5a+2b-c (iv) a-b-3c
This is a Further Maths question
help the correct answer or I will report​

Answer 1

$\quad \huge \quad \quad \boxed{ \tt \:Answer }$

$\qquad \tt \rightarrow \: 2a + 3b - c = 13i+16j+ 14k$

$\qquad \tt \rightarrow \: a - 2b + 4c = 16i+ 3j- 22k$

$\qquad \tt \rightarrow \: 5a + 2b - c = 14i+ 21j- 5k$

$\qquad \tt \rightarrow \: a - b - 3c = - 21i - 7j - 8k$

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$\large \tt Solution \: :$

$\qquad \large \rm \: (i) \: 2a + 3b - c$

$\qquad \tt \rightarrow \: 2(2i + 3j - 4k) + 3(5i + 4j + 7k) - (6i + 2j - k)$

$\qquad \tt \rightarrow \: 4i + 6j - 8k + 15i + 12j + 21k- 6i - 2j + k$

$\qquad \tt \rightarrow \: (4i + 15i -6i )+( 6j + 12j - 2j) + (- 8k + 21k + k )$

$\qquad \tt \rightarrow \: 13i+16j+ 14k$

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$\qquad \large \rm \: (ii) \: a - 2b + 4c$

$\qquad \tt \rightarrow \: (2i + 3j - 4k) - 2(5i + 4j + 7k) + 4(6i + 2j - k)$

$\qquad \tt \rightarrow \: 2i + 3j - 4k -10i - 8j - 14k + 24i + 8j - 4k$

$\qquad \tt \rightarrow \:( 2i - 10i + 24i)+ (3j -8j + 8j ) + ( - 4k - 14k - 4k)$

$\qquad \tt \rightarrow \:16i+ 3j - 22k$

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$\qquad \large \rm \: (iii) \:5 a + 2b - c$

$\qquad \tt \rightarrow \: 5(2i + 3j - 4k) + 2(5i + 4j + 7k) - (6i + 2j - k)$

$\qquad \tt \rightarrow \: 10i + 15j - 20k + 10i + 8j + 14k - 6i - 2j + k$

$\qquad \tt \rightarrow \:( 10i + 10i - 6i )+ (15j + 8j - 2j) + (- 20k + 14k + k )$

$\qquad \tt \rightarrow \:14i+ 21j- 5k$

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$\qquad \large \rm \: (iv) \: a -b -3c$

$\qquad \tt \rightarrow \: (2i + 3j - 4k) - (5i + 4j + 7k) -3 (6i + 2j - k)$

$\qquad \tt \rightarrow \: 2i + 3j - 4k - 5i - 4j - 7k -18i - 6j + 3 k$

$\qquad \tt \rightarrow \: (2i - 5i - 18i) +( 3j - 4j - 6j ) + (- 4k - 7k + 3 k)$

$\qquad \tt \rightarrow \: - 21i - 7j - 8k$

Answered by : ❝ AǫᴜᴀWɪᴢ ❞