CBSE 2024 · Region 3 · Set 1 · Q24 · 2 marks
Find the position vector of point C which divides the line segment joining points $\displaystyle A$ and $\displaystyle B$ having position vectors $\displaystyle \hat{i}+2 \hat{j}-\hat{k}$ and $\displaystyle -\hat{i}+\hat{j}+\hat{k}$ respectively in the ratio $\displaystyle 4: 1$ externally. Further, find $\displaystyle |\overrightarrow{\mathrm{AB}}|:|\overrightarrow{\mathrm{BC}}|$.
Marking-scheme solution
Position vector of $\displaystyle C=\vec{r}=\frac{4 \vec{b}-\vec{a}}{3}$\text { i.e. } \vec{r}=\frac{1}{3}(-5 \hat{i}+2 \hat{j}+5 \hat{k})Now, $\displaystyle \overrightarrow{A B}=-2 \hat{i}-\hat{j}+2 \hat{k} \Rightarrow|\overrightarrow{A B}|=3$\overrightarrow{B C}=-\frac{1}{3}(2 \hat{i}+\hat{j}-2 \hat{k}) \Rightarrow|\overrightarrow{B C}|=1$\displaystyle |\overrightarrow{A B}|:|\overrightarrow{B C}|=3: 1$
Vector AlgebraMultiplication of a Vector by a ScalarApplyvery_short_answermedium
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CBSE Class 12 Mathematics past-paper question from the 2024board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.