AP EAMCET · Maths · Vector Algebra
\(\mathbf{a}=3 \hat{\mathbf{i}}+\hat{\mathbf{j}}-\hat{\mathbf{k}}, \mathbf{b}=\hat{\mathbf{i}}-4 \hat{\mathbf{j}}+5 \hat{\mathbf{k}}, \mathbf{c}=4 \hat{\mathbf{i}}+5 \hat{\mathbf{j}}-\hat{\mathbf{k}}\) are three vectors and a vector \(\mathbf{r}\) is perpendicular to both the vectors \(\mathbf{b}\) and \(\mathbf{c}\). If \(\mathbf{r} \cdot \mathbf{a}=9\), then \(\mathbf{r}=\)
- A \(3(\hat{\mathbf{i}}-\hat{\mathbf{j}}-\hat{\mathbf{k}})\)
- B \(3(\hat{\mathbf{i}}-\hat{\mathbf{j}}+\hat{\mathbf{k}})\)
- C \(9(\hat{\mathbf{i}}-\hat{\mathbf{j}}-\hat{\mathbf{k}})\)
- D \(9(\hat{\mathbf{i}}-\hat{\mathbf{j}}+\hat{\mathbf{k}})\)
Answer & Solution
Correct Answer
(A) \(3(\hat{\mathbf{i}}-\hat{\mathbf{j}}-\hat{\mathbf{k}})\)
Step-by-step Solution
Detailed explanation
Given vectors \(\mathbf{a}=3 \hat{\mathbf{i}}+\hat{\mathbf{j}}-\hat{\mathbf{k}}, \mathbf{b}=\hat{\mathbf{i}}-4 \hat{\mathbf{j}}+5 \hat{\mathbf{k}}\) and \(\mathbf{c}=4 \hat{\mathbf{i}}+5 \hat{\mathbf{j}}-\hat{\mathbf{k}}\)…
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- \(\mathrm{A}(1,15), \mathrm{B}(3,-12), \mathrm{C}(6,12)\) are three consecutive turning points of a continuous curve \(y=f(x)\). If \(f(x)=0\) only for \(x=\alpha\) and \(x=\beta\), then \(|\beta-\alpha| < \)AP EAMCET 2023 Hard
- In a \(\triangle A B C\), if \(\frac{2 r_2 r_3}{r_2-r_1}=r_3-r_1\), then \(\frac{r_1\left(r_2+r_3\right)}{\sqrt{r_1 r_2+r_2 r_3+r_3 r_1}}=\)AP EAMCET 2019 Easy
- If \(\sin \alpha=\sin \beta\) and \(\cos \alpha=\cos \beta\), then \(\alpha-\beta=\) for some integer \(n\).AP EAMCET 2020 Easy
- If the increase in the side of square is \(6 \%\), then the approximate percentage increase in its area ......AP EAMCET 2020 Easy
- The value of isAP EAMCET 2021 Medium
- The binomial coefficients which are in decreasing order areAP EAMCET 2004 Easy
More PYQs from AP EAMCET
- One mole of \(\mathrm{C}_2 \mathrm{H}_5 \mathrm{OH}(l)\) was completely burnt in oxygen to form \(\mathrm{CO}_2(\mathrm{~g})\) and \(\mathrm{H}_2 \mathrm{O}(l)\). The standard enthalpy of formation \(\left(\Delta_f \mathrm{H}^{\ominus}\right)\) of \(\mathrm{C}_2 \mathrm{H}_5 \mathrm{OH}(l), \mathrm{CO}_2(\mathrm{~g})\) and \(\mathrm{H}_2 \mathrm{O}(l)\) is \(x, y, z \mathrm{~kJ} \mathrm{~mol}^{-1}\) respectively. What is \(\Delta_r \mathrm{H}^{\ominus}\) (in \(\mathrm{kJ} \mathrm{mol}^{-1}\) ) for this reaction?AP EAMCET 2025 Medium
- Let \(\bar{a}=2 \bar{i}+\bar{j}-\bar{k}\) and \(\bar{b}=\bar{i}+3 \bar{k}\).
If \(\bar{c}\) is a unit vector, then the maximum value of \(\left[\begin{array}{lll}\bar{a} & \bar{b} & \bar{c}\end{array}\right]\) isAP EAMCET 2017 Easy - If \(f(x)=x^{\operatorname{Sec}^{-1} x}\), then \(f^{\prime}(2)=\)AP EAMCET 2025 Medium
- Let \(A=\left[\begin{array}{cc}1 & 3 \\ 4 & -3\end{array}\right]\),
Let \(S=\left\{\left[\begin{array}{l}x \\ y\end{array}\right] \in R^2 / A\left[\begin{array}{l}x \\ y\end{array}\right]=3\left[\begin{array}{l}x \\ y\end{array}\right]\right\}\) what is the cardinality of \(S\) ?AP EAMCET 2021 Medium - An object of mass \(2 \mathrm{~kg}\) is attached to a spring with spring constant \(8 \mathrm{Nm}^{-1}\). If the object is executing simple harmonic motion then the number of cycles it completes in \(66 \mathrm{~s}\) isAP EAMCET 2022 Easy
- The energies required to set up in a cube of side \(10 \mathrm{~cm}\)
(i) a uniform electric field of \(10^7 \mathrm{Vm}^{-1}\) and
(ii) a uniform magnetic field of \(0.25 \mathrm{Wbm}^{-2}\) are respectively about
\[
\left(\mu_0=4 \pi \times 10^{-7} \mathrm{Hm}^{-1}, \varepsilon_0=8.9 \times 10^{-12} \mathrm{Fm}^{-1}\right)
\]AP EAMCET 2018 Medium