Question 18 of 68intermediate🔧 ApplyNumerical2 marks

Find the position vector of a point R which divides the line joining two points P and Q whose position vectors are î + 2ĵ - k̂ and -î + ĵ + k̂ respectively, in the ratio 2:1

(i)

internally

Answer

-13i^+43j^+13k^\frac{1}{3} \hat{i} + \frac{4}{3} \hat{j} + \frac{1}{3} \hat{k}

(ii)

externally

Answer

-3i^+3k^\hat{i} + 3 \hat{k}

Explanation

This question applies the section formula for vectors. For internal division, the position vector is (m𝑏 + n𝑎)/(m+n). For external division, it is (m𝑏 - n𝑎)/(m-n). Here, point P has position vector 𝑎 = î + 2ĵ - k̂ and point Q has position vector 𝑏 = -î + ĵ + k̂. The ratio is m:n = 2:1.

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