TS EAMCET · Maths · Vector Algebra
If \(2 \hat{i}-\hat{j}+\hat{k}, \hat{i}-3 \hat{j}-5 \hat{k}\) are the position vectors of the points \(\mathrm{A}\) and \(\mathrm{B}\) respectively, \(\mathrm{C}\) divides \(\mathrm{AB}\) in the ratio \(2: 3\) and \(\mathrm{M}\) is the mid-point of \(\mathrm{AB}\), then 5 (position vector of \(C)-2(\) position vector of \(M)=\)
- A \(5 \hat{i}-5 \hat{j}+3 \hat{k}\)
- B \(11 \hat{i}-13 \hat{j}-11 \hat{k}\)
- C \(5 \hat{i}+5 \hat{j}-3 \hat{k}\)
- D \(11 \hat{i}+13 \hat{j}-11 \hat{k}\)
Answer & Solution
Correct Answer
(A) \(5 \hat{i}-5 \hat{j}+3 \hat{k}\)
Step-by-step Solution
Detailed explanation
P.V. of point A and B are \((2,-1,1)\) and \((1,-3,-5), C\) divides \(A B\) in the ratio \(2: 3\) and \(M\) is the mid-point of \(A B\) \(\Rightarrow 5(\overline{\mathrm{OC}})=(8,-9,-7)\) and \(2(\overline{\mathrm{OM}})=(3,-4,-4)\) Now…
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
- \(E_1\) and \(E_2\) are two independent events of a random experiment with \(P\left(E_1\right)=\frac{1}{2}\) and \(P\left(E_1 \cup E_2\right)=\frac{2}{3}\). Then match the items of List-1 with those of List-II.
The correct match is \(\begin{array}{lllllllll}A & \text { B } & \text { C } & \text { D } & \text { A } & \text { B } & \text { C } & \text { D }\end{array}\)TS EAMCET 2020 Medium - Let \(R-(\alpha, \beta)\) be the range of \(\frac{x+3}{(x-1)(x+2)}\). Then, the sum of the intercepts of the line \(\alpha x+\beta y+1=0\) on the coordinate axis isTS EAMCET 2018 Medium
- Match the functions of List-I with their nature in List-II and choose the correct option.
Then the correct match is
TS EAMCET 2019 Easy - The solution of the differential equation \(\frac{d y}{d x}-2 y \tan 2 x=e^x \sec 2 x\) isTS EAMCET 2013 Easy
- The roots of the equation \(x^3-3 x^2+3 x+7=0\) are \(\alpha\), \(\beta, \gamma\) and \(\omega, \omega^2\) are complex cube roots of unity. If the terms containing \(x^2\) and \(x\) are missing in the transformed equation when each one of these roots is decreased by \(h\), then \(\frac{\alpha-h}{\beta-h}+\frac{\beta-h}{\gamma-h}+\frac{\gamma-\mathrm{h}}{\alpha-\mathrm{h}}=\)TS EAMCET 2024 Hard
- If \(\frac{2 x+1}{(x-1)^2\left(x^2+1\right)}=\frac{A}{x-1}+\frac{B}{(x-1)^2}+\frac{C x+D}{x^2+1}\), then \(A+B+C+D=\)TS EAMCET 2020 Easy
More PYQs from TS EAMCET
- In molecule, the hybridizations of carbon and oxygen atoms are respectivelyTS EAMCET 2020 Easy
- Two vibrating strings ' ' and ' ' produce beats of frequency . The beat frequency is found to reduce to if the tension in the string is slightly reduced. If the original frequency of is , then the frequency of ' isTS EAMCET 2021 Medium
- If and thenTS EAMCET 2021 Easy
- Latent heat of vaporisation of water is . The amount of heat needed to convert of water into vapour at isTS EAMCET 2020 Easy
- Consider an amplifier circuit in which a transistor is used in common-emitter mode. The load resistance \(3 \mathrm{k} \Omega\). When a signal of \(30 \mathrm{mV}\) is added to base emitter voltage, the base current is changed by \(30 \mu \mathrm{A}\) and the collector current is changed by \(3 \mathrm{~mA}\). The power gain in this circuit will beTS EAMCET 2019 Medium
- Match the following.
The correct match is \(\text { A } \quad B \quad C\)qTS EAMCET 2021 Hard