R divides the line joining two points P and Q whose position vectors are \stackrel{\^}{i}+2 \stackrel{\^}{j}-{k^{\^}} and -\stackrel{\^}{i}+ \stackrel{\^}{j}+\stackrel{\^}{k} respectively in the ratio 2: 1 externally . S divides P Q internally in the ratio 2: 1. Then the position vector of the midpoint of the line joining R and S is ______

Correct Answer is : −53^i+23^j+53^k

\frac{-5}{3} \stackrel{\^}{i}-\frac{2}{3} \stackrel{\^}{j}-\frac{5}{3} \stackrel{\^}{k}

\frac{-5}{3} \stackrel{\^}{i}+\frac{2}{3} \stackrel{\^}{j}+\frac{5}{3} \stackrel{\^}{k}

\frac{ 5}{3} \stackrel{\^}{i}-\frac{2}{3} \stackrel{\^}{j}-\frac{5}{3} \stackrel{\^}{k}

\frac{5}{3} \stackrel{\^}{i}+\frac{2}{3} \stackrel{\^}{j}+\frac{5}{3} \stackrel{\^}{k}

AP EAPCET 24-Aug-2021 Shift 2 Paper

Section: Mathematics

Question : 29 of 160

Marks: +1, -0

R divides the line joining two points P and Q whose position vectors are

−

and −

respectively in the ratio 2:1 externally .S divides PQ internally in the ratio 2:1. Then the position vector of the midpoint of the line joining R and S is ______

−5
3
^
i
−
2
3
^
j
−
5
3
^
k
−5
3
^
i
+
2
3
^
j
+
5
3
^
k
5
3
^
i
−
2
3
^
j
−
5
3
^
k
5
3
^
i
+
2
3
^
j
+
5
3
^
k

Validate

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