Find the scalar and vector components of the vector with initial point (2,1) and terminal point (-5,7).
Find the scalar and vector components of the vector with initial point (2,1) and terminal point (-5,7).
Solution and Explanation
The vector with the initial point P(2,1) and Q(-5,7) can be given by,
\(\overrightarrow{PQ}\) = \((-5-2)\hat i+(7-1)\hat{j}\)
\(⇒\)\(\overrightarrow{PQ}\) = \(-7\hat i+6\hat{j}\)
Hence, the required scalar components are -7 and 6 while the vector components are \(-7\hat i\)and \(6\hat{j}\).
Top Questions on Vector Algebra
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Questions Asked in CBSE CLASS XII exam
- Find the inverse of each of the matrices, if it exists. \(\begin{bmatrix} 1 & 3\\ 2 & 7\end{bmatrix}\)
- For what values of x,\(\begin{bmatrix} 1 & 2 & 1 \end{bmatrix}\)\(\begin{bmatrix} 1 & 2 & 0\\ 2 & 0 & 1 \\1&0&2 \end{bmatrix}\)\(\begin{bmatrix} 0 \\2\\x\end{bmatrix}\)=O?
- Find the inverse of each of the matrices,if it exists \(\begin{bmatrix} 2 & 1 \\ 7 & 4 \end{bmatrix}\)
What is the Planning Process?
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- Find the inverse of each of the matrices,if it exists. \(\begin{bmatrix} 2 & 3\\ 5 & 7 \end{bmatrix}\)
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.