For the vectors shown in the figure, determine (Figure...

For the vectors shown in the figure, determine (Figure 1) the magnitude of $\vec{B} - 3\vec{A}$. Express your answer using three significant figures. $\vec{B} - 3\vec{A} = 109$ units Part B the direction of $\vec{B} - 3\vec{A}$. Express your answer using three significant figures. $\theta = 13.9$ below $-x$ axis Part C the magnitude of $2\vec{A} - 3\vec{B} + 2\vec{C}$. Express your answer using three significant figures.

Transcript

00:01 So here it is given that the two vectors having the magnitude, let's say a vector is equal to 44 .0, while the second vector, c vector is given 31 .0.

00:16 And we need to find, and c vector is given, okay, 26 .5.

00:23 And we need to calculate the difference of vector that is a minus of c.

00:29 So how did we calculate that? so basically, these both of the vectors will have the two components, and their one one component will give us the required resultant, right? so let's draw the diagram first.

00:45 So let's say this is the x axis, this is the y axis, okay? now onto the x axis, there will be one component of a that is a cosine of 28 degree, because it is given into the diagram, the angle was 28 degree, okay? then this y component will be a sine of 28 degree, a sine of 28 degree.

01:13 So a will be along this direction at an angle of 28 degree, okay? this is what a we have been given.

01:22 While the, okay, sorry, this c vector is having the magnitude of 31 .0, okay? now according to the question, c is along the negative of y direction.

01:35 So as we wanted to subtract here, so we can consider this into the direction of positive y axis.

01:43 So let's say this is nothing but c vector.

01:46 So in x direction, the magnitude can be given by, let's say x would be equals to a cos of 28 degree.

01:55 So this will be equals to 44 cos of 28 degree, will comes out equals to 38 .85.

02:03 Now similarly, along the y direction, the magnitude will be y, that will be equals to c plus a sine of 28 degree.

02:15 So that will be equals to 31 plus 44 cos, sorry, sine of 28 degree.

02:22 So it will comes out 51 .66...

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