Let, \(a=i-j+2k\). Then the vector in the direction of a with magnitude \(5\) units is ?
Let, \(a=i-j+2k\). Then the vector in the direction of a with magnitude \(5\) units is ?
\(5i-5j+10k\)
\(-5i-5j+10k\)
\(\dfrac{1}{√6}[5i-5j+10k]\)
\(\dfrac{1}{√6}[10i-5j+5k]\)
The Correct Option is C
Solution and Explanation
Given that
\( a =i-j+2k\)
Then, first find magnitude of \(a\)
\(|a|=√(1^{2}+(-1)^{2}+2^{2})\)
\(=√6\)
Then the unit vector in the direction of a is
\(=\) \(\dfrac{1}{√6}[i-j+2k]\)
as per the question the vector having a magnitude of 5
\(=\)\(\dfrac{1}{√6}[5i-5j+10k]\) (Ans.)
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Concepts Used:
Multiplication of a Vector by a Scalar
When a vector is multiplied by a scalar quantity, the magnitude of the vector changes in proportion to the scalar magnitude, but the direction of the vector remains the same.
Properties of Scalar Multiplication:
The Magnitude of Vector:
In contrast, the scalar has only magnitude, and the vectors have both magnitude and direction. To determine the magnitude of a vector, we must first find the length of the vector. The magnitude of a vector formula denoted as 'v', is used to compute the length of a given vector ‘v’. So, in essence, this variable is the distance between the vector's initial point and to the endpoint.