Question 217: Laws of Motion

Question

If $$\overrightarrow F  = 2\widehat i + \widehat j - \widehat k$$ and $$\overrightarrow r  = 3\widehat i + 2\widehat j - 2\widehat k$$, then the scalar and vector products of $$\overrightarrow F $$ and $$\overrightarrow r $$ have the magnitudes respectively as

Accepted Answer

Given, $$\overrightarrow F  = 2\widehat i + \widehat j - \widehat k$$ and $$\overrightarrow r  = 3\widehat i + 2\widehat j - 2\widehat k$$
$$\overrightarrow F \,.\,\overrightarrow r  = 2(3) + 2(1) + ( - 2)( - 1)$$
$$ = 6 + 2 + 2 = 10$$
$$\overrightarrow F  	imes \overrightarrow r  = \left| {\matrix{
   {\widehat i} & {\widehat j} & {\widehat k}  \cr 
   2 & 1 & { - 1}  \cr 
   3 & 2 & { - 2}  \cr

} } ight|$$
$$ = \widehat i( - 2 + 2) - \widehat j( - 4 + 3) + \widehat k(4 - 3)$$
$$ \Rightarrow \overrightarrow F  	imes \overrightarrow r  = \widehat j + \widehat k$$
$$|\overrightarrow F  	imes \overrightarrow r | = \sqrt {{1^2} + {1^2}}  = \sqrt 2 $$

Answer

10, 2

Answer

5, $$\sqrt 3 $$

Answer

4, $$\sqrt 5 $$

Answer

10, $$\sqrt 2 $$

Laws of Motion

If $\overrightarrow F = 2\widehat i + \widehat j - \widehat k and \overrightarrow r = 3\widehat i + 2\widehat j - 2\widehat k, then the scalar and vector products of \overrightarrow F and \overrightarrow r $ have the magnitudes respectively as

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