Question

Let a=5i+7j and b= 10i+8j be two vectors.A . draw and lebel the above vectors in 2D coordinates frame on a grid graph paper.B.in the above 2D coordinates frames, show how to add the two vectors by drawing using parallelogram method. Measure the magnitude and and direction cosine of the sun vectors drawn and show their numbers.C. Calculate the sum of the two vectors using component methods. What is the calculate magnitude and direction ( angle cosine) of the vector?

Answer 1

We will have the following:

A:

B. We will have that in order to add the vectors, we will have:

So, the total sum of the vectors is:

So, the resultig vector is:

$15i+15j$

It's magnitude:

$d=\sqrt[]{(15-0)^2+(15+0)^2}\Rightarrow d=15\sqrt[]{2}\Rightarrow d\approx21.2$

So, the magnitude of the vector is 15sqrt(2) units, that is approximately 21.2 units.

We will have that its direction is:

$\cos (\theta)=\frac{15}{15\sqrt[]{2}}\Rightarrow\theta=\cos ^{-1}(\frac{1}{\sqrt[]{2}})$$\Rightarrow\theta=45$

So, its direction is 45° counterclockwise.

C. Using component vector methods, we will have:

$V=(5i+7j)+(10i+8j)\Rightarrow V=15i+15j$

The magnitude is:

$|V|=\sqrt[]{(15i)^2+(15j)^2}\Rightarrow|V|=15\sqrt[]{2}$

The direction is given by:

$\cos (\theta)=\frac{a\cdot b}{|a|\cdot|b|}\Rightarrow\theta=\cos ^{-1}(\frac{a\cdot b}{|a|\cdot|b|})$$\Rightarrow\theta=\cos ^{-1}(\frac{1}{\sqrt[]{2}})\Rightarrow\theta=45$

So, the direction is again 45°.