AP EAMCET · Maths · Three Dimensional Geometry
If the direction cosines of a line are \(\left(\frac{a}{\sqrt{83}}, \frac{5}{\sqrt{83}}, \frac{c}{\sqrt{83}}\right)\) and \(c-a=4\), then \(c a=\)
- A \(24\)
- B \(21\)
- C \(18\)
- D \(33\)
Answer & Solution
Correct Answer
(B) \(21\)
Step-by-step Solution
Detailed explanation
Direction cosine of \(a \hat{i}+b \hat{j}+c \hat{k}\) can be \(\frac{a}{\sqrt{a^2+b^2+c^2}}, \frac{b}{\sqrt{a^2+b^2+c^2}}, \frac{c}{\sqrt{a^2+b^2+c^2}}\) According to question, \(\sqrt{a^2+b^2+c^2}=\sqrt{83}, b=5\) \(\Rightarrow \quad a^2+(5)^2+c^2=83\)…
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
- If \(f: R \rightarrow[-1,1]\) and \(g: R \rightarrow A\) are two surjective mappings and \(\sin \left(g(x)-\frac{\pi}{3}\right)=\frac{f(x)}{2} \sqrt{4-f^2(x)}\), then \(A=\)AP EAMCET 2018 Hard
- The number of points in the interval \((0,2)\) at which \(f(x)=|x-0.5|+|x-1|+\tan x\) is not differentiable isAP EAMCET 2019 Easy
- If the incentre of the triangle formed by the lines \(x-2=0, x+y-1=0\), \(x-y+3=0\) is \((\alpha, \beta)\), then \(\beta=\)AP EAMCET 2025 Medium
- Suppose \(A B O C\) is a rhombus in the first quadrant with \(O\) being the origin. If the vertices \(B\) and \(C\) of \(\triangle A B C\) lie respectively on \(y=\frac{4}{3} x\) and \(y=0\) and the side \(B C\) passes through \(\left(\frac{2}{3}, \frac{2}{3}\right)\), then the mid-point of \(B C\) isAP EAMCET 2022 Easy
- If is the perpendicular bisector of the line segment joining the points and , then the value of equals_____AP EAMCET 2021 Medium
- For a Poisson distribution, if mean \(=l\), variance \(=m\) and \(l+m=8\), then \(e^4[1-P(X>2)]=\)AP EAMCET 2022 Medium
More PYQs from AP EAMCET
- If a microscope is placed in air, the minimum separation of two objects seen as distinct is 6 pm . If the same is placed in a medium of refractive index 1.5 , then the minimum separation of the two objects to see as distinct isAP EAMCET 2024 Medium
- If \(\omega\) is a complex cube root of unity, then \(\sin \left\{\left(\omega^{10}+\omega^{23}\right) \pi-\frac{\pi}{4}\right\}\) is equal toAP EAMCET 2008 Medium
- If \(\mathrm{E}\) and \(\mathrm{F}\) are events such that \(P(\bar{F})=0.7\) and \(P(E \cap F)=0.2\), then \(\mathrm{P}(E \mid F)\) isAP EAMCET 2022 Easy
- If one of the roots of the equation \(x^2+p x+q=0\) is equal to the square of the other thenAP EAMCET 2021 Easy
- Magnetic field at the centre of a circular loop of area \(A\) is \(B\). Then the magnetic moment of the loop is
(\(\mu_0\)-permeability of the free space)AP EAMCET 2019 Easy - Four positive point charges are kept at the four corners of a square of side . The net electric field at the midpoint of any one side of the square is take )AP EAMCET 2018 Easy