You Have Learned Of Two Fundamental Units That Are Not Vector Quantities. Which Are They?

Annotation:A vector is represented by assuming and italic notations similar " A "

Question: Is a vector necessarily changed if it is rotated through an angle?
Solution: Not necessarily, a vector changes if it  is rotated through any angle except for "2π, 4π, 6π, …… radians "

Q: Is it possible to add together two vectors of unequal magnitude and go zero? Is it possible to add together three vectors of equal magnitude and get Zero?
Solution: Sum of two vectors can just be nada if they are equal in magnitude and opposite in direction. So no, two vector of unequal magnitude cannot be added to requite null vector.
Three vectors of equal magnitude and making an angle 120 degrees with each other gives a zero resultant.

Q: Does the phrase "Direction of zero vector" accept physical significance? Talk over in terms of velocity, force etc.
Solution: Although the being of nothing vector is essential for vector algebra equally it acts as the essential additive inverse, there is no physical significance of null vector. Really its direction is undeterminable.
If a man applies 0 N of forcefulness, he is not applying whatsoever force and then its direction can't perhaps have any physical significance.

Q: Tin you add together three unit vectors to become a unit vector? Does your answer change if two unit vectors are along the coordinate axes?
Solution: Of course nosotros tin can add together three unit of measurement vectors to give a unit vector. An instance of this is i , i , -i
even If any ii unit vectors are forth the axes the tertiary vector can so be aligned then that they give a vector of unit magnitude. I volition give you lot an example: i , j , – i

Q: Can you lot have physical quantity having magnitude and management which are not vectors
Solution:Yes, Electric current is such quantity that has got both magnitude and direction but is non a vector.

Q: Which of the two statements  is more advisable?
(a) Two forces are added using triangle rule considering force is a vector quantity
(b) Force is a vector quantity because two forces are added using the triangle rule
Solution: The second statement (b) is more appropriate because The definition of a vector is "A quantity which contains information about both direction and magnitude and obeys laws of vector algebra". Force will only exist defined as a vector quantity if it can exist added using triangle rule.

Q: Can you add 2 vectors representing physical quantities having different dimensions? Can you lot multiply ii vectors representing concrete quantities having unlike dimensions?
Solution: Two quantities can not be added or subtracted if they have dissimilar dimensions exist it a vector or a scalar quantity. But they can exist multiplied or divided, or merely multiplied in the case of vectors.

Q: Can a vector have zero component forth a line and still have nonzero magnitude?
Solution: Yes, any vector has zero component along the direction perpendicular to it. Like, A vector along x-axis has zero component along Y-axis.

Q: Allow α and β exist the angles made exist Aand -A with the positive X-axis. Testify that Tanα = Tanβ. Thus, giving Tanθ does not uniquely determine the direction of A.
Solution: If a vector A makes α with x-axis then -A makes an angle (π+α) = β with aforementioned positive direction of 10-axis
==> Tanβ = Tan(π+α) = Tanα……..QED
So aye if we simply give Tanθ of a vector where θ is the angle made past the x-axis, it doesn't uniquely make up one's mind the management of a vector.

Q: Is the vector sum of i and j a unit vector ? If no can you multiply this sum by a scalar number to get a unit of measurement vector?
Solution: No, Their sum has a magnitude of sqrt(ii), and so apparently it is not a unit vector. Only if nosotros multiply the sum with ane/sqrt(2) it becomes a unit vector.

Q: Let A = 3 i + four j . Write four vectors B such that A  ≠ B only A = B.
Solution: This vector A has a magnitude = 5
and then take a vector
Start putting different values of θ in the above vector you tin can get equally many vector as you lot want satisfying the condition
A  ≠ B but A=B

Q: Can you lot have A  × B = A  • B with A ≠ 0 and B ≠ 0? what if one of the two vectors is nil?
Solution: Never, considering A × B is a vector quantity and A • B is a scalar quantity and a vector tin never be equated to a scalar, fifty-fifty if their magnitudes are zero. So even if  one of the two vectors is zero A × B gives a null vector and A • B is merely null.

Q: If A  × B =0, can you say that (a) A = B , (b) A ≠ B?
Solution: We can't definitely say either of them is true because the two vectors can have unlike or same magnitudes but if they are parallel to each other their cross product is always zero.

Q: Let A = v i -4 j and B = -vii.five i + 6 j .
(a) Exercise nosotros have B = grand A
(b) tin we say yard= B / A
Solution:
(a) yes, If you multiply (-ane.v) to A you get B
==> B =-1.5 A
(b) Simply that doesn't hateful -i.5 = B / A , Because division of a vector with another vector is non defined.

You Have Learned Of Two Fundamental Units That Are Not Vector Quantities. Which Are They?,

Source: https://microphysicsdaily.wordpress.com/2015/08/22/chapter-2-physics-and-mathematics/

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