Question

Show that a =9i+j-6k and b =4i-6j+5k are at right angles to each other

Answer 1

SOLUTION

TO PROVE

$\vec{a} = 9 \hat{i} + \hat{j} - 6 \hat{k} \: \: and \: \: \vec{b} = 4 \hat{i} - 6 \hat{j} + 5 \hat{k}$

are at right angle to each other

PROOF

Here the given two vectors are

$\vec{a} = 9 \hat{i} + \hat{j} - 6 \hat{k} \: \: and \: \: \vec{b} = 4 \hat{i} - 6 \hat{j} + 5 \hat{k}$

Now

$\vec{a}.\vec{b}$

$= ( 9 \hat{i} + \hat{j} - 6 \hat{k}). (4 \hat{i} - 6 \hat{j} + 5 \hat{k})$

$= 36 - 6 - 30$

$= 0$

Hence the given two vectors are perpendicular

Hence the given two vectors are at right angles to each other

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