AP EAMCET · Maths · Three Dimensional Geometry
The point of intersection of the lines represented by \(\mathbf{r}=(\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-\hat{\mathbf{k}})+\lambda(2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+4 \hat{\mathbf{k}})\) and \(\mathbf{r}=(-\hat{\mathbf{i}}-3 \hat{\mathbf{j}}+7 \hat{\mathbf{k}})+\mu(\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-\hat{\mathbf{k}})\) is
- A \(3 \hat{\mathbf{i}}+5 \hat{\mathbf{j}}+3 \hat{\mathbf{k}}\)
- B \(5 \hat{\mathbf{i}}+8 \hat{\mathbf{j}}+7 \hat{\mathbf{k}}\)
- C \(-\hat{\mathbf{i}}-\hat{\mathbf{j}}-5 \hat{\mathbf{k}}\)
- D \(-3 \hat{\mathbf{i}}-4 \hat{\mathbf{j}}-9 \hat{\mathbf{k}}\)
Answer & Solution
Correct Answer
(A) \(3 \hat{\mathbf{i}}+5 \hat{\mathbf{j}}+3 \hat{\mathbf{k}}\)
Step-by-step Solution
Detailed explanation
Let point \(P\) is the point of intersection of given lines \(\mathbf{r}=(\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-\hat{\mathbf{k}})+\lambda(2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+4 \hat{\mathbf{k}})\) and…
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
- Match the following columns.
Column I Column 11 (A) The centroid of the triangle formed by (2, 3,-1), (5, 6, 3),(2,-3,1) is (p) (2,2,2) (B) The circumcentre of the triangle formed by (1, 2, 3), (2, 3, 1),(3, 1, 2) is (q) (3, 1, 4) (C) The orthocentre of the triangle formed by (2, 1, 5), (3, 2, 3), (4, 0, 4) is (r) (1, 1, 0) (D) The incentre of the triangle formed by (0, 0, 0), (3, 0, 0), (4, 0, 4) is (s) (3, 2, 1) (E) The incentre of the triangle formed by (0, 0, 0), (3, 0, 0), (4, 0, 4) is (t) (0, 0, 0) AP EAMCET 2015 Hard - Box \(A\) contains 2 black and 3 red balls, while Box \(B\) contains 3 black and 4 red balls. Out of these two boxes one is selected at random; and the probability of choosing Box \(A\) is double that of Box \(B\). If a red ball is drawn from the selected box, then the probability that it has come from Box \(B\), isAP EAMCET 2005 Medium
- If , thenAP EAMCET 2021 Medium
- If the equation of the polar of the point \((\alpha,-1)\) with respect to the circle \(x^2+y^2-4 x-6 y-12=0\) is \(y=\beta\), then \(4(\alpha+\beta)=\)AP EAMCET 2025 Medium
- A line \(L\) passes through the point \(P(1,2)\) and makes an angle of \(60^{\circ}\) with \(\overrightarrow{O X}\) in the positive direction. \(A\) and \(B\) are two points lying on \(L\) at a distance of 4 units from P. If 0 is the origin, then the area of \(\triangle 0 \mathrm{AB}\) isAP EAMCET 2025 Medium
- If \(\mathrm{A}=\left\{\mathrm{x} / 9 \mathrm{x} \geq \mathrm{x}^2+20\right\}\) and \(\mathrm{f}: \mathrm{A} \rightarrow \mathrm{R}\) is defined by \(f(x)=2 x^3-15 x^2+36 x-48\), then the maximum value of \(f(x)\) isAP EAMCET 2023 Medium
More PYQs from AP EAMCET
- The sum of the order and degree of the differential equation \(\frac{d^4 y}{d x^4}=\left\{c+\left(\frac{d y}{d x}\right)^2\right\}^{\frac{3}{2}}\) isAP EAMCET 2024 Easy
- \(\int_0^2 x^8\left(\frac{4}{x^2}-1\right)^{5 / 2} d x=\)AP EAMCET 2025 Medium
- If \(\int \frac{d x}{\cos ^4 x+\sin ^4 x}=\frac{1}{\sqrt{2}} \tan ^{-1}[g(x)]+C\), then \(g(x)\) equalsAP EAMCET 2021 Medium
- If and then the sum of all values of satisfying the equation isAP EAMCET 2021 Medium
- Which quantity among the following has neither units nor dimensions?AP EAMCET 2021 Easy
- If \(\mathbf{a}, \mathbf{b}, \mathbf{c}\) and \(\mathbf{r}\) are vectors such that \(\mathbf{a}\) is not perpendicular to \(\mathbf{b} \cdot \mathbf{r} \times \mathbf{b}=\mathbf{c} \times \mathbf{b}\) and \(\mathbf{r} \cdot \mathbf{a}=\mathbf{0}\) then \(\mathbf{r}=\)AP EAMCET 2020 Medium