AP EAMCET · Maths · Vector Algebra
If \(\overrightarrow{\mathbf{a}}, \overrightarrow{\mathbf{b}}, \overrightarrow{\mathbf{c}}\) are three non-coplanar vectors, then the vector equation \(\overrightarrow{\mathbf{r}}=(1-p-q) \overrightarrow{\mathbf{a}}+p \overrightarrow{\mathbf{b}}+q \overrightarrow{\mathbf{c}}\) represents a :
- A straight line
- B plane
- C plane passing through the origin
- D sphere
Answer & Solution
Correct Answer
(B) plane
Step-by-step Solution
Detailed explanation
We have, \(\overrightarrow{\mathbf{r}}=(1-p-q) \overrightarrow{\mathbf{a}}+p \overrightarrow{\mathbf{b}}+q \overrightarrow{\mathbf{c}}\) where \(p, q\) are scalars. It represents an equation of the plane.
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
- In \(P\) and \(Q\) are square matrices such that \(P^{2006}=0\) and \(P Q=P+Q\), then \(\operatorname{det}(Q)\) will beAP EAMCET 2020 Medium
- If A \((1,0,2), \mathrm{B}(2,1,0), \mathrm{C}(2,-5,3), \mathrm{D}(0,3,2)\) are four points and the point of intersection of the lines AB and CD is \(\mathrm{P}(a, b, c)\), then \(a+b+c=\)AP EAMCET 2024 Medium
- There are 10 points in a plane, out of these 6 are collinear. If \(N\) is the total number of triangles formed by joining these points, then \(N=\)AP EAMCET 2022 Easy
- If \(M\) is the foot of the perpendicular drawn from the origin to the line \(x-2 y+3=0\) which meets the \(X\) and \(Y\)-axes at \(A\) and \(B\) respectively, then \(A M=\)AP EAMCET 2025 Medium
- The solution of the differential equation \(x \frac{d y}{d x}=y-x \tan \left(\frac{y}{x}\right)\) is (Here, \(k\) is an arbitrary constant)AP EAMCET 2019 Medium
- The distance between the parallel lines \(9 x^2-6 x y+y^2+18 x-6 y+8=0\) isAP EAMCET 2020 Medium
More PYQs from AP EAMCET
- At the temperature for the reaction . Gibbs energy change for the reaction is
Assume are ideal gasesAP EAMCET 2018 Easy - The magnetic field at the centre \(\mathrm{C}\) of the arrangement shown in figure is
AP EAMCET 2019 Easy - Given the function then is equal toAP EAMCET 2021 Easy
- A metal surface is illuminated by a light of given intensity and frequency to cause photoemission. If the intensity of illumination is reduced to one-fourth of its original value, then the maximum kinetic energy of the emitted photoelectrons would becomeAP EAMCET 2020 Medium
- Which of the following statements is not correct?
(i) Froth-floatation is used for removing gangue from sulphide ore.
(ii) Cresols are used to stabilise the froth.
(iii) Sodium cyanide can be used as depressant for preferential separation.
(iv) Aniline can be used as froth enhancer.AP EAMCET 2020 Medium - If a line \(A B\) of length \(r\) moves so that \(A\) and \(B\) always lie respectively on \(X\)-axis and \(y=6 x\), then the locus of mid-point of \(A B\) isAP EAMCET 2022 Hard