A¯$$=8i^$$−$$6j^$$ ; B¯$$=$$−$$6i^$$−$$xj^$$ are perpendicular vectors then x is $$_______$$

A¯$$=8i^$$−$$6i^$$ ; B¯$$=$$−$$6i^$$−$$xj^$$ A¯.B¯$$=0$$ $$(8i^$$−$$6j^)($$−$$6i^$$−$$xj^)=0$$ −$$48+6x=0$$⇒$$6x=48$$⇒$$x=8$$

Scalars and Vectors

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Question

$\bar{A} = 8 \hat{i} - 6 \hat{j}; \bar{B} = - 6 \hat{i} - x \hat{j}$ are perpendicular vectors then x is _______

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Solution

$\bar{A} = 8 \hat{i} - 6 \hat{i}; \bar{B} = - 6 \hat{i} - x \hat{j}$
$\bar{A} . \bar{B} = 0$

$(8 \hat{i} - 6 \hat{j}) (- 6 \hat{i} - x \hat{j}) = 0$

$- 48 + 6 x = 0 \Rightarrow 6 x = 48 \Rightarrow x = 8$

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