AP EAMCET · Maths · Vector Algebra
Let \(\hat{i}-\hat{j}+2 \hat{k}\) and \(\hat{i}+2 \hat{j}-2 \hat{k}\) be the position vectors of points \(\mathrm{A}\) and \(\mathrm{B}\) respectively. If \(\mathrm{C}\) is a point on the line joining \(\mathrm{A}\) and \(\mathrm{B}\) such that \(\mathrm{BC}=10\), then the position vector of \(\mathrm{C}\) can be
- A \(\hat{\mathrm{i}}+8 \hat{\mathrm{j}}-10 \hat{\mathrm{k}}\)
- B \(\hat{i}+4 \hat{j}-6 \hat{k}\)
- C \(\hat{\mathrm{i}}-8 \hat{\mathrm{j}}+10 \hat{\mathrm{k}}\)
- D \(\hat{\mathrm{i}}-4 \hat{\mathrm{j}}-6 \hat{\mathrm{k}}\)
Answer & Solution
Correct Answer
(A) \(\hat{\mathrm{i}}+8 \hat{\mathrm{j}}-10 \hat{\mathrm{k}}\)
Step-by-step Solution
Detailed explanation
\(\overrightarrow{\mathrm{OA}}=\hat{\mathrm{i}}-\hat{\mathrm{j}}+2 \hat{\mathrm{k}}, \overrightarrow{\mathrm{OB}}=\hat{\mathrm{i}}+2 \hat{\mathrm{j}}-2 \hat{\mathrm{k}}\)…
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
- Observe the following statements
A. Integrating factor of \(\frac{d y}{d x}+y=x^2\) is \(e^x\)
R. Integrating factor of \(\frac{d y}{d x}+P(x) y=Q(x)\) is \(e^{\int P(x) d x}\)
Then, the true statement among the following isAP EAMCET 2004 Easy - The differential equation corresponding to the family of circles given by \((x-a)^2+(y-b)^2=4\), where \(a\) and \(b\) are parameters, isAP EAMCET 2017 Hard
- If in a \(\triangle A B C, s(s-a)=(s-b)(s-c)\), thenAP EAMCET 2021 Easy
- Let \(f\) be a non-zero real valued continuous function satisfying \(f(x+y)=f(x) \cdot f(y)\) for all \(x, y \in \mathbb{R}\). If \(f(2)=9\), then \(f(6)\) is equal toAP EAMCET 2013 Easy
- If the image of the point \(A(1,1,1)\) with respect to the plane \(4 x+2 y+4 z+1=0\) is \(\mathrm{B}(\alpha, \beta, \gamma)\), then \(\alpha+\beta+\gamma=\)AP EAMCET 2025 Medium
- If PS is the median of the triangle with vertices \(\mathrm{P}(2,2)\), \(\mathrm{Q}(6,-1)\) and \(\mathrm{R}(7,3)\), then the equation of the line passing through \((1,-1)\) and parallel to PS isAP EAMCET 2023 Easy
More PYQs from AP EAMCET
- If \(\frac{d}{d x}\left(A \log \left(\frac{\sqrt{1-x^3}+B}{\sqrt{1-x^3}+1}\right)\right)=\frac{1}{x \sqrt{1-x^3}}\), then \(A B=\)AP EAMCET 2022 Hard
- The solution of the differential equation represents a family ofAP EAMCET 2021 Easy
- Which of the following is a favourable factor for cation formation?AP EAMCET 2004 Easy
- Calculate the area enclosed by the curvesAP EAMCET 2020 Easy
- If \(a\) and \(b(a>b)\) are points of discontinuity of the function
\[
f(x)=\left\{\begin{array}{ccc}
3-2 x^2, & \text { for } & x \leq 0 \\
2 x+3, & \text { for } & 0 < x \leq 1 \\
2 x^2-3 x, & \text { for } & 1 < x < 2 \\
2 x-3, & \text { for } & 2 \leq x < 3 \\
|x|, & \text { for } & x \geq 3
\end{array}\right.
\]
then \(3 a-b=\)AP EAMCET 2018 Medium - How many chords can be drawn through points on a circle?AP EAMCET 2022 Easy