AP EAMCET · Maths · Vector Algebra
Let \(\mathbf{a}, \mathbf{b}\) and \(\mathbf{c}\) be three non-coplanar vectors. The vector equation of a line which passes through the point of intersection of two lines, one joining the points \(\mathbf{a}+2 \mathbf{b}-5 \mathbf{c}\), \(-\mathbf{a}-2 \mathbf{b}-3 \mathbf{c}\) and the other joining the points \(-4 \mathbf{c}, 6 \mathbf{a}-4 \mathbf{b}+4 \mathbf{c}\) is
- A \(r=2 a-4 b+3 c+\mu(a-6 b+4 c)\)
- B \(r=3 a+6 b-c+\mu(a+2 b+c)\)
- C \(\mathbf{r}=2 \mathrm{a}+3 \mathrm{~b}-\mathrm{c}+\mu(\mathrm{a}+\mathbf{b}-\mathbf{c})\)
- D \(r=-2 b+3 c+\mu(a-4 b+3 c)\)
Answer & Solution
Correct Answer
(B) \(r=3 a+6 b-c+\mu(a+2 b+c)\)
Step-by-step Solution
Detailed explanation
Equation of line joining the points, \(\mathbf{a}+2 \mathbf{b}-5 \mathbf{c},-\mathbf{a}-2 \mathbf{b}-3 \mathbf{c}\) is \[ \mathbf{r}=(\mathbf{a}+2 \mathbf{b}-5 \mathbf{c})+\lambda_1,(2 \mathbf{a}+4 \mathbf{b}-2 \mathbf{c}) \] Similarly, equation of the line joining the points…
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
- AP EAMCET 2022 Medium
- If \(A=\left\{x \in[0,2 \pi] / \tan x-\tan ^2 x>0\right\}\) and \(B=\left\{x \in[0,2 \pi] /|\sin x| < \frac{1}{2}\right\}\), then \(A \cap B=\)AP EAMCET 2018 Medium
- If the equation
\(3 x^2+7 x y+2 y^2+2 g x+2 f y+2=0\) represents
a pair of intersecting lines and the square of the distance of their point of intersection from the origin is \(\frac{2}{5}\), then \(f^2+g^2=\)AP EAMCET 2018 Medium - If the value of then the value ofAP EAMCET 2020 Medium
- If the straight line passing through \(P(3,4)\) makes an angle \(\frac{\pi}{6}\) with the positive \(x\)-axis in anticlockwise direction and meets the line \(12 x+5 y+10=0\) at Q , then the length of the segment PQ isAP EAMCET 2024 Medium
- The scalar product of the vector with a unit vector along the sum of the vectors and is equal to one. Then.AP EAMCET 2020 Medium
More PYQs from AP EAMCET
- Consider the following statements :
I : If \(a\) and \(b\) are positive real numbers, then \(\sqrt{-a} \times \sqrt{-b}=\sqrt{a b}\)
II : The argument of \(\frac{1+i \sqrt{3}}{1-i \sqrt{3}}\) is \(120^{\circ}\)
ThenAP EAMCET 2017 Medium - Which of the following statements is not correct?AP EAMCET 2017 Medium
- If \(f(x)=\sin x+\cos x\), then \(f\left(\frac{\pi}{4}\right) f^{(i v)}\left(\frac{\pi}{4}\right)\) is equal toAP EAMCET 2010 Easy
- Let \(A=\left[\begin{array}{cccc}1 & 0 & -1 & -3 \\ 0 & 1 & 1 & k-1 \\ 0 & 0 & k-1 & 1\end{array}\right]\) and \(k \in R\). Then, the value of \(k\), if exists, for which the rank of \(A\) is 2 , isAP EAMCET 2022 Medium
- If the chord of contact of the point \(\mathrm{P}(\mathrm{h}, \mathrm{k})\) with respect to the circle \(x^2+y^2-4 x-4 y+8=0\) meets the circle in two distinct points and it also makes an angle \(45^{\circ}\) with the positive \(\mathrm{X}\)-axis in the positive direction, then \((\mathrm{h}, \mathrm{k})\) cannot beAP EAMCET 2023 Easy
- For equality of functions \(f\) and \(g \ldots . . .\).
(i) domain of \(f=\operatorname{domain}\) of \(g\)
(ii) \(f(x)=g(x)\)
(iii) \(x \in \operatorname{domain}\) of \(f\)AP EAMCET 2020 Easy