Question

two forces p and q acting at a point are such that if p is reversed , the direction of the resultant is turned through 90 . then p = nQ . find the value of n​

Answer 1

Answer:

Explanation:

N=90*2

180

Hopes

Answer 2

Answer:

The 2 vectors can be represented by:

p = aî + bĵ

q = cî + dĵ

The resultant is q+p = (c+a)î + (d+b)ĵ

If p is reversed it becomes -p. So the new resultant is q-p.

q-p = (c-a)î + (d-b)ĵ

q+p is perpendicular to q-p so their dot (scalar) product is zero:

((c+a)î + (d+b)ĵ) • ((c-a)î + (d-b)ĵ) = 0

(c+a)(c-a) + (d+b)(d-b) = 0

c² - a² + d² - b² = 0

a²+b² = c² + d²

Since ||p||²= a²+b² and ||q||²= c²+d²

||p|| = ||q||

So the magnitude of p must equal the magnitude of q, but p can be in any direction (but see note below).

______________

Note. There is an exception to the direction of p. p and q can't be parallel or antiparallel, as either p-q or p+q would then be zero. Taking a dot product where one of the vectors is zero is not an allowed operation.

Explanation:

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