TS EAMCET · Maths · Three Dimensional Geometry
The magnitude of the projection of the vector \(\mathbf{a}=4 \mathbf{i}-3 \mathbf{j}+2 \mathbf{k}\) on the line which makes equal angles with the coordinate axes is
- A \(\sqrt{2}\)
- B \(\sqrt{3}\)
- C \(\frac{1}{\sqrt{3}}\)
- D \(\frac{1}{\sqrt{2}}\)
Answer & Solution
Correct Answer
(B) \(\sqrt{3}\)
Step-by-step Solution
Detailed explanation
Let the vector \(\mathbf{v}\) make an angle \(\alpha\) with each of the three axes, then direction cosine of \(\mathbf{v}\) are \( \) Also, \(\quad \cos ^2 \alpha+\cos ^2 \alpha+\cos ^2 \alpha=1\) Hence, direction cosine of \(\mathbf{v}\) are \( \) or \( \) So, the required line…
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
- \(\int_0^3\left(\sin \left(\frac{\pi}{3} x\right)-\cos \left(\frac{\pi}{3} x\right)\right) d x=\)TS EAMCET 2022 Hard
- \(\int_{\pi / 5}^{3 \pi / 10} \frac{d x}{\sec ^2 x+\left(\tan ^{2022} x-1\right)\left(\sec ^2 x-1\right)}=\)TS EAMCET 2024 Hard
- \(x=\log \left(\frac{1}{y}+\sqrt{1+\frac{1}{y^2}}\right) \Rightarrow y\) is equal toTS EAMCET 2012 Easy
- The coordinates of a point on the curve \(x=a(\theta+\sin \theta), y=a(1-\cos \theta)\) where the tangent is inclined at an angle \(\frac{\pi}{4}\) to the positive \(X\)-axis, areTS EAMCET 2019 Medium
- \(\int(\log x)^3 x^4 d x\)TS EAMCET 2018 Easy
- Let \(M\) be the foot of the perpendicular from a point \(P\) on the parabola \(y^2=8(x-3)\) onto its directrix and let \(S\) be the focus of the parabola. If \(\triangle S P M\) is an equilateral triangle, then \(P\) is equal toTS EAMCET 2010 Hard
More PYQs from TS EAMCET
- A cube of side \(L\) has point charges \(+q\) located at its seven vertices and \(-q\) at remaining one vertex. The electric field at its centre is found to be \(|\mathbf{E}|=\alpha\left(\frac{q}{4 \pi \varepsilon_0 L^2}\right)\). The magnitude of constant \(\alpha\) is
TS EAMCET 2020 Medium - Identify the pair of drugs which act as tranquilizersTS EAMCET 2023 Easy
- Assertion : The zeroth law of thermodynamics leads to the concept of temperature. Reason : The zeroth law states that two systems in thermal equilibrium with a third system are in thermal equilibrium with each other. The correct option among the following isTS EAMCET 2022 Easy
- If \(e^{i t}=\cos t+i \sin t\) and \(e^{-i t}=\cos t-i \sin t\) then \(\cos \mathrm{h}\) \((x+i y)-\cosh (x-i y)=\)TS EAMCET 2022 Hard
- \(\text { In a } \triangle A B C, \frac{\Delta^2}{a^2+b^2+c^2}\left(\frac{1}{r_1^2}+\frac{1}{r_2^2}+\frac{1}{r_3^2}+\frac{1}{r^2}\right)=\)TS EAMCET 2020 Medium
- The maximum value of \(\frac{\log x}{x}, 0 < x < \infty\) isTS EAMCET 2009 Medium