Question

Find the unit of vectors 1) a = i+2j-2k 2) b = 3i+2j-k​

Answer 1

Answer:

1) a = i+2j-2k

$magnitude = \sqrt{1 {}^{2} + 2 {}^{2} + ( - 2) {}^{2} }$

$= \sqrt{1 + 4 + 4}$

$= \sqrt{9 } = 3$

unit vector = 1/3 (1i + 2j - 2k)

= 1/3 i + 2/3 j - 2/3 k

2) b = 3i+2j-k

$magnitude = \sqrt{3 {}^{2} + 2 {}^{2} + ( - 1) {}^{2} }$

$= \sqrt{9 + 4 + 1}$

$= \sqrt{14}$

unit vector = 1/√14( 3i+2j-k)

= 3/√14 i + 2/√14 j - 1/√14 k

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