Question

For the three vectors the magnitude of D=A-B-C
and its direction are
B-4
A-1
(a) 25._459. below ve, X-axis
() 13, 57° above +ve, x-axis
(C) 5, 530, below + ve, X-axis
(d) 36, 45 above + ve, X-axis​

Answer 1

Given :  D=A-B-C

To Find :   magnitude of D and its direction

(a) 25,  45°. below +ve, X-axis

() 13, 57° above +ve, x-axis

(C) 5, 53°, below + ve, X-axis

(d) 36, 45° above + ve, X-axis​

Solution:

A = 1  along x axis

B =  4 along y axis

C = 2 along - x axis  = - 2 along x axis

D = A  - B  -  C

=  1  along x axis  -  4 along y axis - (-2) along x axis

= 3 along x axis  -  4 along y axis

Hence Magnitude =  √3² + 4²   = 5

Magnitude =   5

tan α   =  - 4/3    α is  in 4th Quadrant ( as y is -ve and x is + ve  )

=>  α  = - 53°

Hence 53° below +ve x axis

So correct answer is 5 ,  53° below +ve x axis

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Answer 2

from the above figure we can say that the answer is the magnitude is 5 and 53 degrees below the positive x axis