Question

Angel between the vectors i-2j+k and 4i-3j-4k is

Answer 1

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Angle between,

$\hat{i} - 2 \hat{j} + \hat{k} \\ and \\ 4 \hat{i} - 3 \hat{j} - 4 \hat{k}$

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Angle between two vectors is given by =>

$\implies \cos( \Theta) = \frac{a.b}{ |a| . |b| } \\ \\ \implies \cos( \Theta) = \frac{ ( \hat{i} - 2 \hat{j} + \hat{k})(4 \hat{i} - 3 \hat{j} - 4 \hat{k})}{ \sqrt{1 + 4 + 1} . \sqrt{16 + 9 + 16} } \\ \\ \implies \cos( \Theta) = \frac{4 - 6 - 4}{ \sqrt{6} . \sqrt{41} } \\ \\ \implies \huge \boxed{ \cos( \Theta) = \frac{ - 6}{ \sqrt{246} } }$

• Note

1. i.i = j. j = k. k = 1
2. i.j = i. k = j. k = i
3. i×i = j×j = k×k = 0
4. i×j = k, k×i = j, j×k = i
5. j×i = -k , i×k = -j , k×j = -i