Given:
Step 1: Placing Points and
Since is on the positive -axis and is isosceles with , the coordinates of can be represented as:
The angle implies that the line makes an angle of with the positive -axis. Thus, the slope of line is:
Let the coordinates of be . Since and , we can use the distance formula to find and the coordinates of .
Step 2: Calculating the Lengths
The length of is given by:
Similarly, the length of is also .
Given that , we find the coordinates of such that it satisfies the isosceles condition and the length of .
Step 3: Equation of Line
The line can be represented in the form:
where is the slope and is the intercept. Using the coordinates of and , we can find the equation of line .
Step 4: Intersection with Line
The line intersects the line at . Substituting the equation of into and solving for and gives the required values.
Step 5: Calculating
After finding and , we compute:
Given that the solution yields:
Conclusion: The value of is 36.
Match the following List-I with List-II and choose the correct option: List-I (Compounds) | List-II (Shape and Hybridisation) (A) PF (I) Tetrahedral and sp (B) SF (III) Octahedral and spd (C) Ni(CO) (I) Tetrahedral and sp (D) [PtCl] (II) Square planar and dsp
Let A be a 3 × 3 matrix such that . If , then is equal to: