WBJEE · Physics · Mathematics in Physics
\(\vec{A}\) and \(\vec{B}\) are two vectors given by \(\vec{A}=2 \hat{i}+3 \hat{j}\) and \(\vec{B}=\hat{i}+\hat{j}\). The magnitude of the component of \(\vec{A}\) along \(\vec{B}\) is
- A \(\frac{5}{\sqrt{2}}\)
- B \(\frac{3}{\sqrt{2}}\)
- C \(\frac{7}{\sqrt{2}}\)
- D \(\frac{1}{\sqrt{2}}\)
Answer & Solution
Correct Answer
(A) \(\frac{5}{\sqrt{2}}\)
Step-by-step Solution
Detailed explanation
Magnitude of components of \(\vec{A}\) along \(\vec{B}=\frac{\vec{A} \cdot \vec{B}}{|\vec{B}|}=\frac{(2 \hat{i}+3 \hat{j})(\hat{i}+\hat{j})}{\sqrt{2}}=\frac{5}{\sqrt{2}}\)
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 Physics
- A parallel plate capacitor is charged and then disconnected from the charging battery. If the plates are now moved farther apart by pulling at them by means of insulating handles, thenWBJEE 2014 Medium
- A circular disc rolls on a horizontal Iloor without slipping and the centre of the disc moves with a uniform velocity \(v\). Which of the following values of the velocily at a point on the rim of the disc can have?WBJEE 2015 Medium
- In an experiment on a circuit as shown in the figure, the voltmeter shows \(8 \mathrm{~V}\) reading. The resistance of the voltmeter is,
WBJEE 2023 Easy - The minimum force required to start pushing a body up a rough (having co-efficient of friction \(\mu\) ) inclined plane is \(\vec{F}_1\) while the minimum force needed to prevent it from sliding is \(\vec{F}_2\). If the inclined plane makes an angle \(\theta\) with the horizontal such that \(\tan \theta=2 \mu\), then the ratio \(F_1 / F_2\) isWBJEE 2025 Medium
- If \(\hat{n}_1, \hat{n}_2\) and \(\hat{t}\) represent, unit vectors along the incident ray, reflected ray and normal to the surface respectively, then
WBJEE 2024 Easy - One mole of a monoatomic ideal gas undergoes a quasistatic process, which is depicted by a straight line joining points \(\left(V_{0}, T_{0}\right)\) and \(\left(2 V_{0}, 3 T_{0}\right)\) in a \({V} \cdot T\) diagram. What is the value of the heat capacity of the gas at the point \(\left(V_{0}, T_{0}\right) ?\)WBJEE 2018 Medium
More PYQs from WBJEE
- The line through the points \((a, b)\) and \((-a,-b)\)
passes through the pointWBJEE 2016 Easy - Water is flowing in streamline motion through a horizontal tube. The pressure at a point in the tube is \(p\) where the velocity of flow is \(v\). At another point, where the pressure is \(p / 2,\) the velocity of flow is [density of water \(=\rho]\)WBJEE 2013 Medium
- The length of the chord of the parabola \(y^{2}=4 a x(a>0)\) which passes through the vertex and makes an acute angle \(\alpha\) with the axis of the parabola isWBJEE 2020 Medium
- The line \(A A^{\prime}\) is on charged infinite \(A\) conducting plane which is perpendicular to the plane of the paper. The plane has a surface density of charge \(\sigma\) and \(B\) is ball of mass \(m\) with a like charge of magnitude \(q . B\) is connected by string from a point on the line \(A A^{\prime}\). The tangent of angle (0) formed between the line \(A A^{\prime}\) and the string is
WBJEE 2015 Hard - Let \(f(x)=x^{13}+x^{11}+x^{9}+x^{7}+x^{5}\)
\(+x^{3}+x+19 .\) Then, \(f(x)=0\) hasWBJEE 2017 Easy - If \(\cos \theta+i \sin \theta, \theta \in \mathbb{R}\), is the root of the equation
\(a_0 x^n+a_1 \cdot x^{n-1}+\ldots .+a_{n-1} x+a_n=0, a_0, a_1, \ldots \ldots . a_n \in \mathbb{R}, a_0 \neq 0\)
then the value of \(a_1 \sin \theta+a_2 \sin 2 \theta+\ldots .+a_n \sin n \theta\) isWBJEE 2024 Medium