Vector $4\hat i + 13\hat j - 18\hat k$ expressed as a linear combination of $\hat i - 2\hat j + 3\hat k$ and $2\hat i + 3\hat j - 4\hat k$ has coefficients $(m, n)$:
A$(2, 3)$
B$(-2, 3)$
C$(3, -2)$
D$(-3, 2)$
Answer & Solution
Correct answer: B. $(-2, 3)$
Set $4\hat i + 13\hat j - 18\hat k = m(\hat i - 2\hat j + 3\hat k) + n(2\hat i + 3\hat j - 4\hat k)$. Equating components: $m + 2n = 4$ and $-2m + 3n = 13$. Solving: $m = -2, n = 3$. Check the $\hat k$ component: $3(-2) - 4(3) = -18$ ✓.
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