enEnglishguગુજરાતી
GUJCET · Maths · Vector Algebra
If \(\vec{a}=\hat{i}+\hat{j}+\hat{k}\) and \(\vec{b}=\hat{i}+2 \hat{j}+3 \hat{k}\) then, \((\vec{a}+\vec{b}) \cdot(\vec{a}-\vec{b})=\) _________ .
- A 11
- B 9
- C -11
- D 9
Answer & Solution
Correct Answer
(C) -11
Step-by-step Solution
Detailed explanation
\(|\vec{a}|^2 = 1^2+1^2+1^2 = 3\) \(|\vec{b}|^2 = 1^2+2^2+3^2 = 1+4+9 = 14\)
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
- The mean and variance of a random variable \(X\) having a binomial distribution are 6 and 3 respectively. The probability of variable \(X\) less than 2 is _________ .GUJCET 2019 Hard
- Area of triangle having vertices \(A (k, 1), B (2,4)\), \(C (1,1)\) is 6 sq. units then \(k=\) __________ .GUJCET 2023 Medium
- If \(x, y \in R\) and \(\left|\begin{array}{lll}\left(a^x+a^{-x}\right)^2 & \left(a^x-a^{-x}\right)^2 & 1 \\ \left(b^x+b^{-x}\right)^2 & \left(b^x-b^{-x}\right)^2 & 1 \\ \left(c^x+c^{-x}\right)^2 & \left(c^x-c^{-x}\right)^2 & 1\end{array}\right|\) \(=2 y+6\) then, \(y=\) _________GUJCET 2019 Medium
- The Area of the region bounded by curve \(y^2=4 x\), Y-axis and line \(y=3\) is __________ sq. units.GUJCET 2021 Easy
- The coordinates of the corner points of the bounded feasible region are \((0,0),(0,40),(20,40),(60,20),(60,0)\). The maximum of the objective function \(z=40 x+30 y\) is ___________ .GUJCET 2025 Easy
- \(\int \frac{e^{2 x}-1}{e^{2 x}+1} d x=\) __________ \(+C\).GUJCET 2024 Hard
More PYQs from GUJCET
- An electric dipole with dipole moment \(4 \times 10^{-9} Cm\) is aligned at \(60^{\circ}\) with direction of a uniform electric field of magnitude \(5 \times 10^4 NC ^{-1}\). Calculate the magnitude of the torque acting on the dipole.GUJCET 2022 Easy
- From which of the following reaction primary amine is produced ?GUJCET 2022 Hard
- An electric dipole of dipole moment \(\overrightarrow{\mathrm{P}}\) is placed parallel to the uniform electric field of intensity \(\overrightarrow{\mathrm{E}}\). On rotating it through angle of \(90^{\circ}\) from this situation, the amount of work done is ___________.GUJCET 2026 Medium
- A galvanometer acting as a voltmeter should have ___________.GUJCET 2014 Hard
- The number of turns in the coil of an AC generator are 100 and its cross sectional area is \(2.5 m^2\). The coil is revolving in a uniform magnetic field of strength 0.3 T with the uniform angular velocity of \(60 rad s ^{-1}\). The value of maximum induced emf is _________ kV.GUJCET 2017 Hard
- What is the correct order for energy of \(d\) orbitals during splitting in Tetra Chlorido Nickelate(II) complex ion?GUJCET 2019 Easy