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A vector A has magnitude a and a^ is a unit vector in the direction of A, then which of the following are correct Multi choice multicorrect. (A) a^=a (B) a^=A/a. (C)A.A=a^2 (D) a=A/a^ I feel the answer should be b and d but in my book it is a,b and c. Pls explain to me if I am wrong.

A vector A has magnitude a and a^ is a unit vector in the direction of A, then which of the following are correct
Multi choice multicorrect.
(A)  a^=a (B) a^=A/a.  
(C)A.A=a^2 (D) a=A/a^
I feel the answer should be b and d but in my book it is a,b and c.
Pls explain to me if I am wrong.

Grade:7

1 Answers

Apoorva Arora IIT Roorkee
askIITians Faculty 181 Points
9 years ago
Let the vector A be represented as
\vec{A}=a\hat{a}
where a is its magnitude and \hat{a}is the unit vector specifying the direction and has magnitude 1.
any unit vector can be calculated as \hat{a}=\frac{\vec{A}}{a}.
So, option b is correct also \vec{A}.\vec{A}=a^{2}since the dot product of a vector with itself will be a scalar quantity and just the square of the magnitude.
So option c is also correct.
option a is wrong as the magnitude of a unit vector is one and not the magnitude of the vector itself also option d is wrong as the magnitude cannot be found out by dividing the vector by its unit vector.
Rather if the vector is \vec{A}=A_{1}i+A_{2}j+A_{3}kthen the magnitude is
a=\sqrt{A_{1}^{2}+A_{2}^{2}+A_{3}^{2}}.

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