Question:
The value of \( m \) if the vectors \( 4i - 3j + 5k \) and \( mi - 4j + k \) are perpendicular, is
The value of \( m \) if the vectors \( 4i - 3j + 5k \) and \( mi - 4j + k \) are perpendicular, is
Show Hint
Perpendicular vectors ⇒ dot product zero. This is one of the fastest vector checks in exams.
Updated On: Apr 30, 2026
- \( -\frac{15}{4} \)
- \( -\frac{17}{4} \)
- \( -\frac{19}{4} \)
- \( 0 \)
- \( \frac{11}{4} \)
Show Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
Concept:
Two vectors are perpendicular if their dot product is zero:
\[
\vec{A} \cdot \vec{B} = 0
\]
Step 1: Write vectors in component form. \[ \vec{A} = (4,-3,5), \vec{B} = (m,-4,1) \]
Step 2: Apply dot product condition. \[ (4,-3,5)\cdot(m,-4,1) = 0 \] \[ 4m + (-3)(-4) + 5(1) = 0 \] \[ 4m + 12 + 5 = 0 \] \[ 4m + 17 = 0 \]
Step 3: Solve for \(m\). \[ 4m = -17 \Rightarrow m = -\frac{17}{4} \]
Step 4: Verification (optional). Substituting back gives dot product = 0, confirming perpendicularity.
Step 1: Write vectors in component form. \[ \vec{A} = (4,-3,5), \vec{B} = (m,-4,1) \]
Step 2: Apply dot product condition. \[ (4,-3,5)\cdot(m,-4,1) = 0 \] \[ 4m + (-3)(-4) + 5(1) = 0 \] \[ 4m + 12 + 5 = 0 \] \[ 4m + 17 = 0 \]
Step 3: Solve for \(m\). \[ 4m = -17 \Rightarrow m = -\frac{17}{4} \]
Step 4: Verification (optional). Substituting back gives dot product = 0, confirming perpendicularity.
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