The point dividing the line segment joining $A(2, -6, 8)$ and $B(-1, 3, -4)$ internally in ratio $1:3$ has coordinates:
A$(5/4, -15/4, 5)$
B$(-7/2, 21/2, -14)$
C$(1/4, -1/4, 2)$
D$(7/2, -21/2, 14)$
Answer & Solution
Correct answer: A. $(5/4, -15/4, 5)$
$\vec r = (1\cdot \vec b + 3\cdot \vec a)/(1+3) = (1(-\hat i+3\hat j-4\hat k) + 3(2\hat i-6\hat j+8\hat k))/4 = (5\hat i -15\hat j +20\hat k)/4$, giving $(5/4, -15/4, 5)$.
Related questions
Vector $PQ$ has magnitude 5 units and is inclined at $150^{\circ}$ to the $x$-axis. In theForces $2i-5j+6k$ and $-i-2j-k$ move a particle from $A(4,-3,-2)$ to $B(6,-1,-3)$. The worPosition vectors $2i-j+k$, $i-3j-5k$ and $3i-4j-4k$ form a triangle with sides $ qrt{41}$,When are two vectors counted as equal?What is the magnitude of the position vector with components 9 and 12?Which two features identify a vector?The work done by a constant force F in displacement d isIf a, b, c are mutually perpendicular unit vectors, the value of a · (b × c) is