JEE Mains · Maths · STD 12 - 10. vector algebra
Consider a \(\Delta A B C\) where \(A(1,3,2), B(-2,8,0)\) and \(C(3,6,7)\). If the angle bisector of \(\angle B A C\) meets the line \(B C\) at \(D\), then the length of the projection of the vector \(\overrightarrow{A D}\) on the vector \(\overrightarrow{A C}\) is :
- A \(\frac{37}{2 \sqrt{38}}\)
- B \(\frac{\sqrt{38}}{2}\)
- C \(\frac{39}{2 \sqrt{38}}\)
- D \(\sqrt{19}\)
Answer & Solution
Correct Answer
(A) \(\frac{37}{2 \sqrt{38}}\)
Step-by-step Solution
Detailed explanation
Given, \(A(1,3,2), B(-2,8,0) \& C(3,6,7)\) And angle bisector of \(\angle B A C\) meets the line \(B C\) at \(D\), Now, plotting the diagram we get, Now, finding \(\overrightarrow{A C}=2 \hat{i}+3 \hat{j}+5 \hat{k}\) \(\Rightarrow|\overrightarrow{A C}|=\sqrt{4+9+25}=\sqrt{38}\)…
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
- If the tangent at \(\left( {1,7} \right)\) to the curve \({x^2} = y - 6\) touches the circle \({x^2} + {y^2} + 16x + 12y + c = 0\) then the value of \(c\) is:JEE Mains 2018 Hard
- If the equation of the plane passing through the line of intersection of the planes \(2 x-7 y+4 z-3=0,3 x-5 y+4 z+11=0\) and the point \((-2,1,3)\) is \(a x+b y+c z-7=0,\) then the value of \(2 a+b+c-7\) isJEE Mains 2021 Hard
- From the base of a pole of height \(20\) meter, the angle of elevation of the top of a tower is \(60^{\circ}\). The pole subtends an angle \(30^{\circ}\) at the top of the tower. Then the height of the tower isJEE Mains 2022 Medium
- A point \(\mathrm{z}\) moves in the complex plane such that \(\arg \left(\frac{\mathrm{z}-2}{\mathrm{z}+2}\right)=\frac{\pi}{4}\), then the minimum value of \(|z-9 \sqrt{2}-2 i|^{2}\) is equal to ..... .JEE Mains 2021 Hard
- If \(A\) and \(B\) are two events such that \(P\left( {A \cup B} \right) = P\left( {A \cap B} \right)\), then the incorrect statement amongst the following statements isJEE Mains 2014 Hard
- Let \(\left(1+x+2 x^{2}\right)^{20}=a_{0}+a_{1} x+a_{2} x^{2}+\ldots+a_{40} x^{40}\) then \(a _{1}+ a _{3}+ a _{5}+\ldots+ a _{37}\) is equal toJEE Mains 2021 Hard
More PYQs from JEE Mains
- Let \(S\) be the set of all real roots of the equation, \(3^{x}\left(3^{x}-1\right)+2=\left|3^{x}-1\right|+\left|3^{x}-2\right| .\) Then \(\mathrm{S}\)JEE Mains 2020 Hard
- Let \(\quad S=\left\{z \in C-\{i, 2 i\}: \frac{z^2+8 i z-15}{z^2-3 i z-2} \in R \right\}\). \(\alpha-\frac{13}{11} i \in S , \alpha \in R -\{0\}\), then \(242 \alpha^2\) is equal toJEE Mains 2023 Hard
- If \(a_r\) is the coefficient of \(x^{10-r}\) in the Binomial expansion of \((1+x)^{10}\), then \(\sum \limits_{r=1}^{10} r^3\left(\frac{a_r}{a_{r-1}}\right)^2\) is equal toJEE Mains 2023 Hard
- The mean and variance of \(7\) observations are \(8\) and \(16\) respectively. If two observations are \(6\) and \(8 ,\) then the variance of the remaining \(5\) observations is:JEE Mains 2021 Medium
- If the distance of the point \(P(43, \alpha, \beta), \beta<0\), from the line \(\vec{r}=4\hat{i}-\hat{k}+\mu(2\hat{i}+3\hat{k}), \mu\in R\) along a line with direction ratios \(3, -1, 0\) is \(13\sqrt{10}\), then \(\alpha^{2}+\beta^{2}\) is equal to ___ .JEE Mains 2026 Medium
- The number of numbers greater than 5000, less than 9000 and divisible by 3, that can be formed using the digits 0, 1, 2, 5, 9, if the repetition of the digits is allowed, is ___ .JEE Mains 2026 Easy