Question

When the result of two vectors is zero? Explaint with the
vectors acting simultaneously on a particle?
What would be the position of a vector when its x-components positive dy
What change is occurred in a vector when it is multiplied by a negative
SHORT ONESTIONS
component is negative? Explain it with the help of a diagram
number?
Give any three examples, when a vector is divided by a scala quantity
Under what circumstances the rectangular components of a vector give some
magnitude?
Can the scalar product of two vector quantities be negative? If your answer
yes, give an example, if no provide a proof?
How scalar product of two vectors obeys commutati
Can any of the two​

Answer 1

Answer:

Yes. A vector is defined by its magnitude and direction, so a vector can be changed by changing its magnitude and direction. If we rotate it through an angle, its direction changes and we can say that the vector has changed.

Page No 27:

ANSWER:

No, it is not possible to obtain zero by adding two vectors of unequal magnitudes.

Example: Let us add two vectors A→ and B→ of unequal magnitudes acting in opposite directions. The resultant vector is given by

R=A2+B2+2ABcosθ−−−−−−−−−−−−−−−−√

If two vectors are exactly opposite to each other, then

θ=180°, cos180°=−1R=A2+B2−2AB−−−−−−−−−−−−−√⇒R=(A−B)2−−−−−−−√⇒R=(A−B) or (B−A)

From the above equation, we can say that the resultant vector is zero (R = 0) when the magnitudes of the vectors A→ and B→ are equal (A = B) and both are acting in the opposite directions.

Yes, it is possible to add three vectors of equal magnitudes and get zero.

Lets take three vectors of equal magnitudes A, −→B→ and C→, given these three vectors make an angle of 120° with each other. Consider the figure below:

Lets examine the components of the three vectors.

Ax=AAy=0Bx=−B cos 60°By=B sin 60°Cx=−C cos 60°Cy=−C sin 60°Here, A=B=CSo, along the x−axis , we have:A−(2A cos 60°)=0, as cos 60°=12 ⇒B sin 60°−C sin 60°=0

Explanation:

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