A straight line cuts off the intercepts $OA = a$ and $OB = b$ on the positive directions of $x$-axis and $y$ axis respectively If the perpendicular from origin $O$ to this line makes an angle of $\frac{\pi}{6}$ with positive direction of $y$-axis and the area of $\triangle O A B$ is $\frac{98}{3} \sqrt{3}$, then $a^2-b^2$ is equal to :
- $\frac{392}{3}$
- $\frac{196}{3}$
- 196
- 98
The Correct Option is A
Solution and Explanation
Or
Comparing both :
Now area of
Top JEE Main Mathematics Questions
- The value of is
- The number of terms of an is even. The sum of the odd terms is and of the even terms is . The last term exceeds the first by . Then the number of terms in the series is ______.
- If , then the general value of is:
- The general solution of
- If the constant term in the binomial expansion of $\left(\frac{x^{\frac{3}{2}}}{2}-\frac{4}{x^l}\right)^9$ is $-84$ and the coefficient of $x^{-3 l}$ is $2^\alpha \beta$, where $\beta<0$ is an odd number, then $|\alpha l-\beta|$ is equal to_____
Top JEE Main Coplanarity of Two Lines Questions
Top JEE Main Questions
- Two masses $m$ and $\frac{m}{2}$ are connected at the two ends of a massless rigid rod of length $l$. The rod is suspended by a thin wire of torsional constant $k$ at the centre of mass of the rod-mass system(see figure). Because of torsional constant $k$, the restoring torque is $\tau =k\theta$ for angular displacement $\theta$. If the rod is rota ted by $\theta_0$ and released, the tension in it when it passes through its mean position will be:
What will be the equilibrium constant of the given reaction carried out in a \(5 \,L\) vessel and having equilibrium amounts of \(A_2\) and \(A\) as \(0.5\) mole and \(2 \times 10^{-6}\) mole respectively?
The reaction : \(A_2 \rightleftharpoons 2A\)- The value of is
- The number of terms of an is even. The sum of the odd terms is and of the even terms is . The last term exceeds the first by . Then the number of terms in the series is ______.
A black body is at a temperature of 2880 K. The energy of radiation emitted by this body with wavelength between 499 nm and 500 nm is U1, between 999 nm and 1000 nm is U2 and between 1499 nm and 1500 nm is U3. The Wien's constant, b = 2.88×106 nm-K. Then,
Concepts Used:
Coplanarity of Two Lines
Condition for Coplanarity Using Cartesian Form
The condition for coplanarity in the Cartesian form appears from the vector form.
Let's consider two points L (a1, b1, c1) & Q (a2, b2, c2) in the Cartesian plane,
Presuppose that there are two vectors q1 and q2. Their direction ratios are subjected by {x1, y1, z1}, and {x2, y2, z2} respectively.
The vector form of equation of the line in connection to L and Q can be stated as under:
LQ = (a2 – a1)i + (b2 – b1)j + (c2 – c1)k
Q1 = x1i + y1j + z1k
Q2 = x2i + y2j + z2k
Condition for Coplanarity Using Vector Form
For the derivation of the condition for coplanarity in vector form, we shall take into consideration the equations of two straight lines to be as stated below:
r1 = l1 + λq1
r2 = l2 + λq2
The condition for coplanarity in vector form is that the line in connection to the two points should be perpendicular to the product of the two vectors, q1 and q2.