Question

Find the position vector of the midpoint of the vector joining the points P(2,3,4) and Q(4,1,−2).

• A. (A) 3i^+2j^+k^
• B. (B) −3i^−2j^−k^
• C. (C) −5i^−3j^−8k^
• D. (D) 5i^−3j^+8k^

Answer 1

Answer: (A)

(A) 3i^+2j^+k^

Answer 2

Explanation:
Given:The position vector of point P=2i^+3j^+4k^Position Vector of point Q=4i^+j^−2k^As we know,The position vector of A(x1,y1,z1) is given byOA→=x1i^+y1j^+z1k^ Compute the position vector of the midpoint of P and Q using the formula:If C(x,y,z) is the midpoint of segment AB→, then we have the position vector of C=OC→=OA→+OB→2=(x1+x22,y1+y22,z1+z22)The position vector of R which divides PQ in half is given by: r→=2i^+3j^+4k^+4i^+j^−2k^2r→=2i^+3j^+4k^+4i^+j^−2k^2r→=6i^+4j^+2k^2=3i^+2j^+k^Hence, the correct option is (A).