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vector a has Magnitude of 5.2 units and is directed east .vector b has a magnitude of 4.3 units and is directed 35 0 of north .By construtig vector diagam. find the magnitude and direction of (a+b)and (b)a-b.

  1. vector a has  Magnitude of 5.2 units and is directed east .vector b has a magnitude of 4.3 units and is directed 350 of north .By construtig vector diagam. find the magnitude and direction of (a+b)and (b)a-b.
 
 
 
 

Grade:12th pass

1 Answers

Arun
25750 Points
5 years ago
\overrightarrow{a} + \overrightarrow{b} is\ 2.7 units\ \widehat{i}\ + 3.5\ units \widehat{j}.Therefore the vector is . = 2.7\ units\ \widehat{i} + 3.5\ units\ \widehat{j}\overrightarrow{a} + \overrightarrow{b} = (5.2 units + (-2.5 units) \widehat{i} + (0\ units + 3.5\ units) \widehat{j}Substituting the above values in equation (3), we haveb_{y} = 3.5 unitsb_{x} = -2.5\ unitsa_{x} = 5.2 unitsFrom equations (1) and (2), we havea_{y} = 0/ units. , we have .\widehat{j}along the unit vector\overrightarrow{a} …… (3)Since there is no component of vector\overrightarrow{a} + \overrightarrow{b} = (a_{x} + b_{x})\widehat{i} + (a_{y} + b_{y}) \widehat{j} is given as:\overrightarrow{b} and vector\overrightarrow{a} that is along west.(a) The addition of vector\widehat{i} indicates that the component points opposite to the direction of unit vector\overrightarrow{b} of vectorb_{x} …… (2)The negative sign in the component\overrightarrow{b} = -2.5 units\ \widehat{i}\ + 3.5\ units\ \widehat{j}\overrightarrow{b} = 4.3 units (-sin35^{\circ}\widehat{j})Substituting the given values, we have\overrightarrow{b} = b (-sin\ \o\ \widehat{i} + cos\ \o\ \widehat{j})\overrightarrow{b} = -b\ sin\ \o \widehat{i} + b\ cos\o \widehat{j}\overrightarrow{a} = b_{x} \widehat{i} + b_{y} \widehat{j} …… (1)The vector is given as:\overrightarrow{a} = 5.2 units\ \widehat{i} is equal to the magnitude of vector that is a .Substituting the given values, we havea_{x}, the value of component\widehat{i}points in the east, along the unit vector \overrightarrow{a} .Since vector \widehat{i} along the unit vector\overrightarrow{a}Where is the component of vector\overrightarrow{a} = a_{x} \widehat{i} as:\overrightarrow{a}Therefore one can write the vector\o = 35^{0}b = 4.3 unitsa = 5.2 unitsGiven:235-2288_Capture.PNG(refer figure below).-bsin\ \phi \widehat{i}is \widehat{i} (say\ b_{y}\widehat{i}) is given as whereas the vector component along the west, opposite to the direction of unit vector \left ( say\ b_{x}\widehat{j} \right )\overrightarrow{j} towards the north, along the unit vector \overrightarrow{b} is represented by a .Therefore the vector component of vector\overrightarrow{a} be represented by b whereas the magnitude of vector\overrightarrow{b}degrees west of north. We also assume that the magnitude of vector\phi is\overrightarrow{b} such that vector\phi is\overrightarrow{b} points toward the east direction (as can be seen from the figure above).We assume that the angle subtended by vector\widehat{i}points towards the north while the unit vector\widehat{j} respectively. The unit vector \widehat{j} and\widehat{i} into its components along the unit vectors\overrightarrow{b}To add the vectors, we need to resolve vector235-1546_chapter 14.png.\overrightarrow{b} vectors and \overrightarrow{a}The figure below shows the vector diagram, representing

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