TS EAMCET · Maths · Vector Algebra
In a triangle ABC, if \(\overline{\mathrm{BC}}=\bar{i}-2 \bar{j}+2 \bar{k}\) and \(\overline{\mathrm{CA}}=6 \bar{i}+3 \bar{j}-2 \bar{k}\), then the perimeter of the triangle is
- A \(5(2+\sqrt{3})\)
- B \(5(2+\sqrt{2})\)
- C \(\sqrt{10}(3+\sqrt{10})\)
- D \(10(2+\sqrt{5})\)
Answer & Solution
Correct Answer
(B) \(5(2+\sqrt{2})\)
Step-by-step Solution
Detailed explanation
\(|\overline{\mathrm{BC}}|=\sqrt{1^2+(-2)^2+2^2}=3\) \(|\overline{\mathrm{CA}}|=\sqrt{6^2+3^2+(-2)^2}=7\) \(\overline{\mathrm{AB}}=-(\overline{\mathrm{BC}}+\overline{\mathrm{CA}})=-((1+6)\bar{i}+(-2+3)\bar{j}+(2-2)\bar{k})=-(7\bar{i}+\bar{j})\)…
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
- The orthocentre of the triangle formed by the points \((1,3),(-3,5)\) and \((5,-1)\) isTS EAMCET 2022 Easy
- \(\cos A=\frac{3}{4} \Rightarrow 32 \sin \left(\frac{A}{2}\right) \sin \left(\frac{5 A}{2}\right)=\)TS EAMCET 2011 Medium
- The equation of the parabola with \(x+2 y=1\) as directrix and \((1,0)\) as focus isTS EAMCET 2023 Medium
- The sum of the coefficients in the expansion of isTS EAMCET 2021 Easy
- If the slope of the tangent drawn at any point \((x, y)\) on the curve \(y=f(x)\) is \(\left(6 x^2+10 x-9\right)\) and \(f(2)=0\), then \(f(-2)=\)TS EAMCET 2024 Easy
- The sides of the rectangle of greatest area that can be inscribed in the ellipse \(x^2+4 y^2=64\) are :TS EAMCET 2006 Hard
More PYQs from TS EAMCET
- The binomial expansion \((7+3 x)^{-2 / 5}\) is valid for all \(x\) in the interval \(\left(\frac{-7}{3}, \frac{7}{3}\right)\) and if the 4 th term of its expansion is \(k x^3\), then \(\left(7^{12 / 5} k\right)=\)TS EAMCET 2020 Easy
- If a circle has its centre on the line and passes through the points of intersection of the two circles and then the centre of that circle isTS EAMCET 2021 Easy
- Assertion (A) The \(\mathrm{pH}\) of a buffer solution containing equal moles of acetic acid and sodium acetate is 4.8 ( \(\mathrm{p} K_a\) of acetic acid is 4.8). Reason (R) The ionic product of water at \(25^{\circ} \mathrm{C}\) is \(10^{-14} \mathrm{~mol}^2 . \mathrm{L}^{-2}\). The correct answer isTS EAMCET 2005 Hard
- A charged particle \((\) charge \(=q\); mass \(=m)\) is rotating in a circle of radius \(R\) with uniform speed \(V\). Ratio of its magnetic moment \((\mu)\) to the angular momentum \((L)\) isTS EAMCET 2016 Easy
- At \(298 \mathrm{~K}\) the molar solubility of \(\mathrm{Cd}(\mathrm{OH})_2\) in \(0.1 \mathrm{M} \mathrm{KOH}\) solution is \(x \times 10^{-\mathrm{y}}\). The values of \(x\) and \(y\) are respectively (at \(298 \mathrm{~K}, \mathrm{~K}_{\mathrm{sp}}\) of \(\mathrm{Cd}(\mathrm{OH})_2=2.5 \times 10^{-14}\) )TS EAMCET 2023 Medium
- If \(\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+3 \hat{\mathbf{k}}, 3 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}+\hat{\mathbf{k}}\) are sides of a parallelogram, then a unit vector is parallel to one of the diagonals of the parallelogram isTS EAMCET 2004 Easy