Question

iv) Find a vector which is parallel to v=i-2j
and has a magnitude 10.​

Answer 1

Answer:

$=\dfrac{10i}{\sqrt{5} } -\dfrac{20j}{\sqrt{5} }$

Explanation:

In the question, the given data is v= i-2j

For this first we need to find unit vector in the direction of vector V.

Unit vector V =$\dfrac{vector (V)}{magnitude V}$

Unit vector$=\dfrac{i-2j}{\sqrt{1^{2} +2^{2} } } \\=\dfrac{i-2j}{\sqrt{1 +4 } }\\=\dfrac{i-2j}{\sqrt{5} }$

Now, all we need to do is to multiply unit vector  with magnitude 10.

vector=$10(\dfrac{i-2j}{\sqrt{5} })$

Required answer is $=\dfrac{10i}{\sqrt{5} } -\dfrac{20j}{\sqrt{5} }$