Given three vectors A = 24i + 33j, B = 55i - 12j and C = 2i + 43j (a) Find the magnitude of each vector. (b) Write an expression for the vector difference A - C. (c) Find the magnitude and direction of the vector difference A-B. (d) In a vector diagram show vector A + B, and A - B, and also show that your diagram agrees qualitatively with your answer.

(a) , .  and .

(b).

(c) and the direction 124.56°.

Explanation:

Given that,

,

and

(a) The magnitude of a vector is the square root of the sum of the square of all the components of the vector, i.e. for a ,.

So, the magnitude of the is

.

The magnitude of the is

.

And, the magnitude of the is

.

(b) The difference between the two vectors is the difference between the corresponding components of the vectors. So, the required expression of is

(c) The expression of is

The magnitude of is

Now, if a vector in 3rd quadrant having direction with respect to direction, than

in the anti-clockwise direction.

Here, from equation (i), for the vector , and .

180°-55.44° [as \pi radian= 180°]

124.56° in the anti-clockwise direction.

(d) Vector diagrams for and has been shown  

in the figure(b) and figure(c) recpectively.

Vector is in 3rd quadrant as calculated in part (c).

While Vector

, which is in 1st quadrant as both the components are position has been shown in figure(b).

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