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  • which of the following is correct? (a) a and p are positive while b and q are negative. (b) a, p, and b are positive while q is negative (c) a, q and b are positive while p is negative (d) a, b, p and q are all positive.

In figure shows the orientation of two vectors u and v in the XY plane.

If u=a\hat{i}+b\hat{j} and

     v=p\hat{i}+q\hat{j}

Which of the following is correct?

(a) a and p are positive while b and q are negative.

(b) a, p, and b are positive while q is negative.

(c) a, q, and b are positive while p is negative.

(d) a, b, p and q are all positive.

Answers (1)

The answer is that option (b) a, p, and b are positive while q is negative.

Explanation:

Now, \vec{u}=a\hat{\iota }+b\hat{J} and \vec{v}=p\hat{\iota }+q\hat{J}

For vector u, both the components a and b are in the positive direction of the x-axis. Hence, they are positive.

For vector v, p is in the positive direction, but q is in the opposite direction. Hence, p is positive, and q is negative.

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