Question

Given a= î + 2j and b=2î +j, what are the magnitudes of the two vectors? Are these two vectors equal?​

Answer 1

Answer:

Two vectors A and B are parallel if and only if they are scalar multiples of one another. A = k B , k is a constant not equal to zero. Two vectors A and B are perpendicular if and only if their scalar product is equal to zero.

Answer 2

Answer:

No, the two vectors are not equal.

The magnitude of a and b vectors is  $\sqrt{5}$.

Explanation:

Magnitude of vector is given by

    $\sqrt{x^{2} +y^{2} +z^{2} }$

where x ,y, z are x, y, z, components of vector.

Given : a = i + 2j

            b= 2i + j

so magnitude of these vectors can be calculate

Magnitude of a vector

 = $\sqrt{1^{2}+2^{2} }$

 = $\sqrt{5}$

Magnitiude of b vector

= $\sqrt{2^{2} + 1^{2} }$

v=$\sqrt{5}$

Hence magnitude of a and b vector is $\sqrt{5}$ .

Now, these two vectors are not equal, if two vectors are equal then their x, y, and z components are also equal.

In the given case magnitude of the two vectors is the same but the vectors are not equal as the x component and y component differ in both the vector.