(A) The vector with the initial point $P(2,1)$ and terminal point $Q(-5,7)$ is given by the displacement vector $\overrightarrow{PQ}$.$\overrightarrow

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Scalar components: $-7, 6$; Vector components: $-7 \hat{i}, 6 \hat{j}$

(A) The vector with the initial point $P(2,1)$ and terminal point $Q(-5,7)$ is given by the displacement vector $\overrightarrow{PQ}$.$\overrightarrow{PQ} = (x_2 - x_1) \hat{i} + (y_2 - y_1) \hat{j}$Substituting the coordinates of $P$ and $Q$:$\overrightarrow{PQ} = (-5 - 2) \hat{i} + (7 - 1) \hat{j}$$\overrightarrow{PQ} = -7 \hat{i} + 6 \hat{j}$Thus,the scalar components are $-7$ and $6$.The vector components are $-7 \hat{i}$ and $6 \hat{j}$.

Class 12 Mathematics Vector Algebra Basic , Modulus and Algebra of vectors

Easy

Find the scalar and vector components of the vector with initial point $(2,1)$ and terminal point $(-5,7).$

A
Scalar components: $-7, 6$; Vector components: $-7 \hat{i}, 6 \hat{j}$
B
Scalar components: $7, -6$; Vector components: $7 \hat{i}, -6 \hat{j}$
C
Scalar components: $-7, 6$; Vector components: $-7 \hat{i}, 6 \hat{j}$
D
Scalar components: $7, 6$; Vector components: $7 \hat{i}, 6 \hat{j}$

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Find the scalar and vector components of the vector with initial point $(2,1)$ and terminal point $(-5,7).$

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