Question:
A particle is displaced from the point \( (2,1,-1) \) to \( (4,3,-4) \) by the force \( 2i + 4j - 5k \). Then the work done by the force is
A particle is displaced from the point \( (2,1,-1) \) to \( (4,3,-4) \) by the force \( 2i + 4j - 5k \). Then the work done by the force is
Show Hint
Always compute displacement carefully; sign mistakes are very common in 3D vectors.
Updated On: Apr 30, 2026
- \( 16 \)
- \( 27 \)
- \( 36 \)
- \( 48 \)
- \( 52 \)
Show Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
Concept:
Work done by a constant force is given by:
\[
W = \vec{F} \cdot \vec{d}
\]
where \( \vec{d} \) is displacement.
Step 1: Find displacement vector. \[ \vec{d} = (4-2,\;3-1,\;-4-(-1)) = (2,2,-3) \]
Step 2: Write force vector. \[ \vec{F} = (2,4,-5) \]
Step 3: Compute dot product. \[ W = (2,4,-5)\cdot(2,2,-3) \] \[ = (2\times2) + (4\times2) + (-5\times -3) \] \[ = 4 + 8 + 15 = 27 \]
Step 4: Interpretation. Positive work indicates force is aiding the motion.
Step 1: Find displacement vector. \[ \vec{d} = (4-2,\;3-1,\;-4-(-1)) = (2,2,-3) \]
Step 2: Write force vector. \[ \vec{F} = (2,4,-5) \]
Step 3: Compute dot product. \[ W = (2,4,-5)\cdot(2,2,-3) \] \[ = (2\times2) + (4\times2) + (-5\times -3) \] \[ = 4 + 8 + 15 = 27 \]
Step 4: Interpretation. Positive work indicates force is aiding the motion.
Was this answer helpful?
0
0
Top KEAM Mathematics Questions
- If $\int e^{2x}f' \left(x\right)dx =g \left(x\right)$, then $ \int\left(e^{2x}f\left(x\right) + e^{2x} f' \left(x\right)\right)dx =$
- The value of $ \cos [{{\tan }^{-1}}\{\sin ({{\cot }^{-1}}x)\}] $ is
- The solutions set of inequation $\cos^{-1}x < \,\sin^{-1}x$ is
- Let $\Delta= \begin{vmatrix}1&1&1\\ 1&-1-w^{2}&w^{2}\\ 1&w&w^{4}\end{vmatrix}$, where $w \neq 1$ is a complex number such that $w^3 = 1$. Then $\Delta$ equals
- Let $p : 57$ is an odd prime number, $\quad \, q : 4$ is a divisor of $12$ $\quad$ $r : 15$ is the $LCM$ of $3$ and $5$ Be three simple logical statements. Which one of the following is true?
View More Questions
Top KEAM Product of Two Vectors Questions
- If $a , \,b$ and $c$ are three non-zero vectors such that each one of them being perpendicular to the sum of the other two vectors, then the value of $| a + b + c |^{2}$ is
- The value of λ for which the vectors \(2i-3j+4k\) and \(-4i+λj-8k\) are collinear is
- Let \( \vec{a} + \vec{b} = \lambda \hat{i} + 16\hat{j} - 18\hat{k} \) and \( \vec{a} - \vec{b} = 2\hat{i} + 8\hat{j} + \lambda \hat{k} \). If \( \vec{a} + \vec{b} \) is perpendicular to \( \vec{a} - \vec{b} \), then \( |\vec{a}| = \)
- If \( |\vec{a}| = 12 \) and the projection of \( \vec{a} \) on \( \vec{b} \) is \( 6\sqrt{3} \), then the angle between \( \vec{a} \) and \( \vec{b} \) is
- Let \( \vec{a} = 6\hat{i} + 2\hat{j} + 3\hat{k} \). If \( \vec{b} \) is parallel to \( \vec{a} \) and \( \vec{a} \cdot \vec{b} = \frac{49}{2} \), then \( |\vec{b}| = \)
View More Questions
Top KEAM Questions
- i.$\quad$ They help in respiration ii.$\quad$ They help in cell wall formation iii.$\quad$ They help in DNA replication iv. $\quad$They increase surface area of plasma membrane Which of the following prokaryotic structures has all the above roles?
- A body oscillates with SHM according to the equation (in SI units), $x = 5 cos \left(2\pi t +\frac{\pi}{4}\right) .$ Its instantaneous displacement at $t = 1$ second is
- The pH of a solution obtained by mixing 60 mL of 0.1 M BaOH solution at 40m of 0.15m HCI solution is
Kepler's second law (law of areas) of planetary motion leads to law of conservation of
- If $\int e^{2x}f' \left(x\right)dx =g \left(x\right)$, then $ \int\left(e^{2x}f\left(x\right) + e^{2x} f' \left(x\right)\right)dx =$
View More Questions