Answer
Verified
478.5k+ views
Hint – In this question we have been given a vector and we have to find a vector which is parallel to the given vector. Parallel means that it must be in the same direction as that of the given vector, so use the concept that a unit vector is always in direction to the vector and is of a magnitude 1. So multiplying it with a scalar quantity alters its length.
Complete step-by-step answer:
Given vector
$5\hat i - \hat j + 2\hat k$.
Let
$\vec a = 5\hat i - \hat j + 2\hat k$
Now we have to find out the vector which is parallel to the given vector and has magnitude 8 units.
As we know when we divide the vector with its modulus then the vector converts into unit vector and when we multiply by 8 with this unit vector the vector converts into the vector which has magnitude 8 units.
Let the parallel vector to the given vector be $\vec x$
$ \Rightarrow \vec x = 8\left( {\dfrac{{\vec a}}{{\left| {\vec a} \right|}}} \right)$……………. (1)
So, first find out the modulus of vector a.
As we know $\vec p = x\hat i + y\hat j + z\hat k$
Then $\left| {\vec p} \right| = \sqrt {{x^2} + {y^2} + {z^2}} $ so, use this property in above equation we have,
$ \Rightarrow \left| {\vec a} \right| = \sqrt {{5^2} + {{\left( { - 1} \right)}^2} + {2^2}} = \sqrt {25 + 1 + 4} = \sqrt {30} $
Now from equation (1) we have,
$ \Rightarrow \vec x = 8\left( {\dfrac{{\vec a}}{{\left| {\vec a} \right|}}} \right) = 8\left( {\dfrac{{5\hat i - \hat j + 2\hat k}}{{\sqrt {30} }}} \right) = \dfrac{{40\hat i - 8\hat j + 16\hat k}}{{\sqrt {30} }}$
$ \Rightarrow \vec x = \dfrac{{40}}{{\sqrt {30} }}\hat i - \dfrac{8}{{\sqrt {30} }}\hat j + \dfrac{{16}}{{\sqrt {30} }}\hat k$
So, this is the required vector which is parallel to the given vector and has magnitude 8 units.
Note – Whenever we face such type of problems the key concept is simply to take out the unit vector of the given vector as it will be in direction to the given vector then multiply it with the scalar constant to obtain the desired magnitude vector.
Complete step-by-step answer:
Given vector
$5\hat i - \hat j + 2\hat k$.
Let
$\vec a = 5\hat i - \hat j + 2\hat k$
Now we have to find out the vector which is parallel to the given vector and has magnitude 8 units.
As we know when we divide the vector with its modulus then the vector converts into unit vector and when we multiply by 8 with this unit vector the vector converts into the vector which has magnitude 8 units.
Let the parallel vector to the given vector be $\vec x$
$ \Rightarrow \vec x = 8\left( {\dfrac{{\vec a}}{{\left| {\vec a} \right|}}} \right)$……………. (1)
So, first find out the modulus of vector a.
As we know $\vec p = x\hat i + y\hat j + z\hat k$
Then $\left| {\vec p} \right| = \sqrt {{x^2} + {y^2} + {z^2}} $ so, use this property in above equation we have,
$ \Rightarrow \left| {\vec a} \right| = \sqrt {{5^2} + {{\left( { - 1} \right)}^2} + {2^2}} = \sqrt {25 + 1 + 4} = \sqrt {30} $
Now from equation (1) we have,
$ \Rightarrow \vec x = 8\left( {\dfrac{{\vec a}}{{\left| {\vec a} \right|}}} \right) = 8\left( {\dfrac{{5\hat i - \hat j + 2\hat k}}{{\sqrt {30} }}} \right) = \dfrac{{40\hat i - 8\hat j + 16\hat k}}{{\sqrt {30} }}$
$ \Rightarrow \vec x = \dfrac{{40}}{{\sqrt {30} }}\hat i - \dfrac{8}{{\sqrt {30} }}\hat j + \dfrac{{16}}{{\sqrt {30} }}\hat k$
So, this is the required vector which is parallel to the given vector and has magnitude 8 units.
Note – Whenever we face such type of problems the key concept is simply to take out the unit vector of the given vector as it will be in direction to the given vector then multiply it with the scalar constant to obtain the desired magnitude vector.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
Mark and label the given geoinformation on the outline class 11 social science CBSE
When people say No pun intended what does that mea class 8 english CBSE
Name the states which share their boundary with Indias class 9 social science CBSE
Give an account of the Northern Plains of India class 9 social science CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Which are the Top 10 Largest Countries of the World?
Give 10 examples for herbs , shrubs , climbers , creepers
Difference Between Plant Cell and Animal Cell
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
Change the following sentences into negative and interrogative class 10 english CBSE
How do you graph the function fx 4x class 9 maths CBSE
Write a letter to the principal requesting him to grant class 10 english CBSE