If the position vectors of A and B are i + 3j | vedclass

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Question

(B) The position vectors are $\vec{OA} = i + 3j - 7k$ and $\vec{OB} = 5i - 2j + 4k$.The vector $\overrightarrow{AB}$ is given by $\vec{OB} - \vec{OA}

Vedclass · Accepted Answer

$-\frac{5}{\sqrt{162}}$

Vedclass · Answer

(B) The position vectors are $\vec{OA} = i + 3j - 7k$ and $\vec{OB} = 5i - 2j + 4k$.The vector $\overrightarrow{AB}$ is given by $\vec{OB} - \vec{OA} = (5-1)i + (-2-3)j + (4 - (-7))k = 4i - 5j + 11k$.The magnitude of $\overrightarrow{AB}$ is $|\overrightarrow{AB}| = \sqrt{4^2 + (-5)^2 + 11^2} = \sqrt{16 + 25 + 121} = \sqrt{162}$.The direction cosine along the $y$-axis is the component of the unit vector along the $y$-direction,which is the coefficient of $j$ divided by the magnitude of the vector.Direction cosine along $y$-axis $= \frac{-5}{\sqrt{162}}$.

If the position vectors of $A$ and $B$ are $i + 3j - 7k$ and $5i - 2j + 4k$,then the direction cosine of $\overrightarrow{AB}$ along the $y$-axis is

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