AP EAMCET · Maths · Vector Algebra
If \(\mathbf{a}, \mathbf{b}\) and \(\mathbf{c}\) are non-zero vectors such \(\mathbf{a} \times \mathbf{b}=\mathbf{c}\) and \(\mathbf{b} \times \mathbf{c}=\mathbf{a}\), then \(\mathbf{a} \times \mathbf{c}\) is
- A equal to \(\mathbf{b}\)
- B parallel to \(\mathbf{b}\)
- C perpendicular to \(\mathbf{b}\)
- D parallel to \(\mathbf{a}\)
Answer & Solution
Correct Answer
(B) parallel to \(\mathbf{b}\)
Step-by-step Solution
Detailed explanation
Given, \(\mathbf{a} \times \mathbf{b}=\mathbf{c}\) and \(\mathbf{b} \times \mathbf{c}=\mathbf{a}\) Here, \(a, b, c\) are mutually perpendicular vectors. \(\therefore \mathbf{a} \times \mathbf{c}\) is parallel to \(\mathbf{b}\).
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
- Let \(a, b\) and \(c\) be positive real numbers. If \(\frac{x^2-b x}{a x-c}=\frac{m-1}{m+1}\) has two roots which are numerically equal but opposite in sign, then the value of \(m\) isAP EAMCET 2021 Easy
- If \(a\) and \(b\) are arbitrary constants, then the differential equation having \(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\) as its general solution isAP EAMCET 2018 Easy
- If \(\overrightarrow{\mathrm{a}}=2 \hat{\mathrm{i}}-\hat{\mathrm{j}}-2 \hat{\mathrm{k}}\) and \(\overrightarrow{\mathrm{b}}=6 \hat{\mathrm{i}}+2 \hat{\mathrm{j}}-3 \hat{\mathrm{k}}\) are two vectors such that \(\vec{a} \cdot \vec{b}\) is minimum, then \(t=\)AP EAMCET 2023 Easy
- If \(f: R \rightarrow R\) is defined by \(f(x)=x-[x]\), where \([x]\) is the greatest integer not exceeding \(x\), then the set of discontinuous of \(f\) isAP EAMCET 2002 Medium
- If \(A\) is a non-zero square matrix of order \(n\) with \(\operatorname{det}(I+A) \neq 0\) and \(A^3=O\), where \(I, O\) are unit and null matrices of order \(n \times n\) respectively, then \((I+A)^{-1}\) is equal toAP EAMCET 2010 Hard
- If \(y=\operatorname{Tan}^{-1}\left(\frac{3 x-x^3}{1-3 x^2}\right)+\operatorname{Tan}^{-1}\left(\frac{7 x}{1-12 x^2}\right)\), then at \(x=0, \frac{d y}{d x}=\)AP EAMCET 2025 Medium
More PYQs from AP EAMCET
- The equation of the circle having the common chord of the circles \(x^2+y^2-8 x=0\) and \(x^2+y^2-9=0\) as its diameter isAP EAMCET 2019 Easy
- How many bijections \(f: \mathbf{Z} \rightarrow \mathbf{Z}\) are there such that \(f(x+y)=f(x)+f(y)\) for all \(x, y \in \mathbf{Z}\) ?AP EAMCET 2020 Easy
- An ideal heat engine operates in Carnot cycle between \(127^{\circ} \mathrm{C}\) and \(27^{\circ} \mathrm{C}\). It absorbs \(5 \times 10^4 \mathrm{cal}\) of heat at higher temperature. Amount of heat converted to work isAP EAMCET 2024 Easy
- \(\left\{x \in R: \frac{14 x}{x+1}-\frac{9 x-30}{x-4} < 0\right\}\) is equal toAP EAMCET 2010 Easy
- A new tetrahedron is formed by joining the centroids of the faces of a given tetrahedron \(O A B C\). Then the ratio of the volume of the new tetrahedron to that of the given tetrahedron isAP EAMCET 2019 Medium
- Let and where denotes the greatest integer less than or equal to thenAP EAMCET 2020 Medium