TS EAMCET · Maths · Vector Algebra
If \(A(4,7,8), B(2,3,4)\) and \(C(2,5,7)\) are the vertices of \(\triangle A B C\), then the length of the internal bisector of the angle \(A\) is
- A \(\frac{1}{2} \sqrt{34}\)
- B \(\frac{1}{3} \sqrt{34}\)
- C \(\frac{2}{3} \sqrt{34}\)
- D \(\frac{3}{8} \sqrt{17}\)
Answer & Solution
Correct Answer
(C) \(\frac{2}{3} \sqrt{34}\)
Step-by-step Solution
Detailed explanation
Given that, points \(A(4,7,8), B(2,3,4)\) and \(C(2,5,7)\) Length \(A B=\sqrt{\left(x_A-x_B\right)^2+\left(y_A-y_B\right)^2+\left(z_A-z_B\right)^2}\) \(=\sqrt{(4-2)^2+(7-3)^2+(8-4)^2}\) \(=\sqrt{(2)^2+(4)^2+(4)^2}=\sqrt{4+16+16}\) \(A B=6\) Length…
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 eccentricity of the conic \(36 x^2+144 y^2-36 x-96 y-119=0\) isTS EAMCET 2004 Easy
- \(\vec{a}, \vec{b}, \vec{c}\) are non-coplanar vectors. If the three points \(\lambda \vec{a}-2 \vec{b}+c, 2 \vec{a}+\lambda \vec{b}-2 \vec{c}, 4 \dot{a}+7 \vec{b}-8 \vec{c}\) are collinear, then \(\lambda=\)TS EAMCET 2024 Easy
- If thenTS EAMCET 2022 Medium
- If the variance of the numbers \(9,15,21, \ldots .,(6 n+3)\) is P, then the variance of the first \(n\) even numbers isTS EAMCET 2025 Hard
- The numbers \(2,3,5,7,11,13\) are written on six distinct paper chits. If 3 of them are chosen at random, then the probability that the sum of the numbers on the obtained chits is divisible by 3 , isTS EAMCET 2024 Hard
- Let \(f: D \rightarrow R, D \subseteq R, c \in D\) and \(r\) be a non zero real number. Consider the following statements: Y. \(c\) is an extreme point of \(f \Rightarrow c\) is an extreme point of \(f f\) M. \(c\) is an extreme point of \(f \Rightarrow c\) is an extreme point of \(r+f\) Which of the following is correct?TS EAMCET 2019 Medium
More PYQs from TS EAMCET
- \(A B C D E F\) is a regular hexagon whose centre is O. Then, \(\mathbf{A B}+\mathbf{A C}+\mathbf{A D}+\mathbf{A E}+\mathbf{A F}\) is equal toTS EAMCET 2016 Easy
- Out of the given 25 consecutive positive integers, three integers are drawn. If the least integer among given 25 integers is an odd number, then the probability that the sum of the three integers drawn is an even number isTS EAMCET 2025 Medium
- Suppose \(\alpha, \beta, \gamma \quad\) are roots of \(x^3+x^2+2 x+3=0\). If \(f(x)=0\) is a cubic polynomial equation whose roots are \(\alpha+\beta, \beta+\gamma, \gamma+\alpha\), then \(f(x)\) is equal toTS EAMCET 2016 Hard
- If the maximum value of \(2 x-7-a x^2\) cannot exceed 20 , then the minimum value of \(a\) isTS EAMCET 2019 Easy
- Let be differentiable function for all and If thenTS EAMCET 2021 Easy
- A projectile is thrown at a speed which is twice its speed at its maximum height. If and are its range and maximum height respectively then the ratio isTS EAMCET 2021 Easy