Question

(vi) Find the x and y components of the resultant of two vectors A and B as shown. given |A|=|B|=10 units​

Answer 1

Given :   two vectors A and B  

|A|=|B|=10 units.​

Vector A is  at 30° angle with x axis

Vector B is  at  105° angle with Vector A

To Find :  x and y components of the resultant of two vectors A and B

Solution:

Vector A is  at 30° angle with x axis

Hence  x component of vector |A| cos 30°

= 10 (√3/2)

= 5√3

y component of vector |A| sin 30°

= 10 (1/2)

= 5

Vector B is  at  105° angle with Vector A

Hence Vector B is  at (105° + 30° = 135°)angle with x axis

Hence  x component of vector |B| cos 135°

= 10 (-1/√2)

= -5√2

y component of vector |B| sin 135°

= 10 (1/√2)

= 5√2

Resultant  x component =  5√3 -5√2  = 5(√3 - √2)

Resultant  y component =  5 + 5√2  = 5(√2 + 1)

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Answer 2

Answer:

Vector A is at 30° angle with x axis

Hence x component of vector IAl cos 30°

= 10 (√3/2) = 5√3

y component of vector IAI sin 30°

= 10 (1/2)

= 5

Vector B is at 105° angle with Vector A

Hence Vector B is at (105° +30° = 135°)angle with x axis

Hence x component of vector IBI cos 135°

= 10 (-1/√2)

= -5√2

y component of vector IBI sin 135°

= 10 (1/√2)

= 5√2

Resultant x component = 5√3-5√2 = 5(√3

- √2)

Resultant y component = 5 +5√2 = 5(√2+1).