The position vectors of points A- B and C are -3- 12- and 11-3- respectively- If C divides the line segment joining A and B in the ratio 3-1- find the values of - and -

[ OA =λî +3ĵ #160;; #160;; OB =12î +μĵ #160;; #160;; OC =11î 3ĵ #160; ] Since, C divides AB in the rati ...

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Standard XII

Mathematics

Section Formula

The position ...

Question

The position vectors of points A, B and C are $λ^i + 3^j, 12^i + μ^j$ and $11^i - 3^j$ respectively. If C divides the line segment joining A and B in the ratio $3 : 1$ , find the values of $λ$ and $μ$ .

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Solution

$\begin{matrix} - - \to O A = λ^i + 3^j - - \to O B = 12^i + μ^j - - \to O C = 11^i - 3^j \end{matrix}$

Since, $C$ divides $A B$ in the ratio $3 : 1$

Therefore,

$\to O C = \frac{3 \to O B + \to O A}{3 + 1}$

$4 \to O C = 3 \to O B + \to O A$

$4 (11^i - 3^j) = 3 (12^i - μ^j) + (λ^i + 3^j)$

$44^i - 12^j = (36 + λ)^i + (3 μ + 3)^j$

$36 + λ 44$

$λ = 8$

And

$3 μ + 3 = - 12$

$μ = - 5$

Therefore,

$λ = 8$ and $μ = - 5$

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The position vectors of points A, B and C are λ^i+3^j,12^i+μ^j and 11^i−3^j respectively. If C divides the line segment joining A and B in the ratio 3:1, find the values of λ and μ.

−−→OA=λ^i+3^j−−→OB=12^i+μ^j−−→OC=11^i−3^jSince, C divides AB in the ratio 3:1 Therefore, →OC=3→OB+→OA3+14→OC=3→OB+→OA4(11^i−3^j)=3(12^i−μ^j)+(λ^i+3^j)44^i−12^j=(36+λ)^i+(3μ+3)^j36+λ44λ=8And 3μ+3=−12μ=−5Therefore, λ=8 and μ=−5

The position vectors of points A, B and C are $λ^i + 3^j, 12^i + μ^j$ and $11^i - 3^j$ respectively. If C divides the line segment joining A and B in the ratio $3 : 1$ , find the values of $λ$ and $μ$ .