Write the Position Vector of a Point Dividing the Line Segment Joining Points Having Position Vectors ^ I + ^ J − 2 ^ K and 2 ^ I − ^ J + 3 ^ K Externally in the Ratio 2:3. - Mathematics

प्रश्न

Write the position vector of a point dividing the line segment joining points having position vectors $\hat{i} + \hat{j} - 2 \hat{k} and 2 \hat{i} - \hat{j} + 3 \hat{k}$ externally in the ratio 2:3.

उत्तर

Let A and B be the points with position vectors $\vec{a} = \hat{i} + \hat{j} - 2 \hat{k}, \vec{b} = 2 \hat{i} - \hat{j} + 3 \hat{k}$ respectively.
Let C divide AB externally in the ratio 2 : 3 such that AC : CB = 2 : 3
∴ Position vector of C = $\frac{2 (2 \hat{i} - \hat{j} + 3 \hat{k}) - 3 (\hat{i} + \hat{j} - 2 \hat{k})}{2 - 3}$
= $\frac{4 \hat{i} - 2 \hat{j} + 6 \hat{k} - 3 \hat{i} - 3 \hat{j} + 6 \hat{k}}{- 1}$
= $\frac{\hat{i} - 5 \hat{j} + 12 \hat{k}}{- 1}$
= $- \hat{i} + 5 \hat{j} - 12 \hat{k}$

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Vectors and Their Types

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Q 25 Q 24 Q 26

पाठ 23: Algebra of Vectors - Very Short Answers [पृष्ठ ७६]

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पाठ 23 Algebra of Vectors
Very Short Answers | Q 25 | पृष्ठ ७६

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Write the Position Vector of a Point Dividing the Line Segment Joining Points Having Position Vectors ^ I + ^ J − 2 ^ K and 2 ^ I − ^ J + 3 ^ K Externally in the Ratio 2:3. - Mathematics

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Write the Position Vector of a Point Dividing the Line Segment Joining Points Having Position Vectors ^ I + ^ J − 2 ^ K and 2 ^ I − ^ J + 3 ^ K Externally in the Ratio 2:3. - Mathematics

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