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  • Provide solution for RD sharma maths class 12 chapter 22 Algebra of Vectors exercise 22.5 question 7

Provide solution for RD sharma maths class 12 chapter 22 Algebra of Vectors exercise 22.5 question 7

Answers (1)

\hat{i}-5\hat{j}

Hint: position vector of point (x , y) is given by  where \hat{i} and \hat{j} are the position in x an y direction.

Given:

               Point A(3,4),B(5,-6),C(4,-1)

Find \vec{a}+2\vec{b}-3\vec{c}

Solution:

As we know position vector of point (x, y) is given by \left (x\hat{i}+y\hat{j} \right )

Where \hat{i}and \hat{j} are the position vector in x and y direction

Then,

\vec{A}=\left (3\hat{i}+4\hat{j} \right )\\ \vec{B}=\left (5\hat{i}+(-6)\hat{j} \right )=5\hat{i}-6\hat{j}\\ \vec{C}=\left (4\hat{i}+(-1)\hat{j} \right )=4\hat{i}-\hat{j}\\ 2\vec{B}=2\left (5\hat{i}-6\hat{j} \right )=10\hat{i}-12\hat{j}\\ 3\vec{C}=3\left (4\hat{i}-\hat{j} \right )=12\hat{i}-3\hat{j}

\vec{a}+2\vec{b}-3\vec{c} Substitute value of \vec{a},2\vec{b},3\vec{c} in equation \vec{a}+2\vec{b}-3\vec{c}

=3\hat{i}+4\hat{j}+10\hat{i}-12\hat{j}-\left ( 12\hat{i}-3\hat{j} \right )\\ =3\hat{i}+4\hat{j}+10\hat{i}-12\hat{j}- 12\hat{i}+3\hat{j}\\ =\hat{i}\left ( 3+10-12 \right )+\hat{j}\left ( 4-12+3 \right )\\ =\hat{i}\left ( 1 \right )+\hat{j}\left ( -5 \right )\\ =\hat{i}-5\hat{j}

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