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Grade 7General Physics

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.

Pushkar Aditya

11 Years agoGrade 7

1 Answer

Apoorva Arora

11 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 $\vec{A}=A_{1}i+A_{2}j+A_{3}k$ then the magnitude is
$a=\sqrt{A_{1}^{2}+A_{2}^{2}+A_{3}^{2}}$ .

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