Correct Answer - c
Statement 2 is true as when the line lies in the plane, vector `vecb` along which the line is directed is perpendicular to the normal `vecc` of...
Correct Answer - B
The equation of the line joining the points (2,-1) and (5,-3) is given by
`y+1 = (-1+3)/(2-5)(x-2)`
` "or " 2x+3y-1 = 0 " " (1)`
Since...
Correct Answer - D
The asymptotes of a rectangular hyperbola are perpendicular to each other.
Given one asymptote
`x+y+c=0`
Let the other asymptote be
`x-y+lambda=0`
We also know that the asymptotes...
Correct Answer - B
`(b)` Since one root is `3`, let
`f(x)=(x-3)(ax+b)`
`implies f(x)=ax^(2)+(b-3a)x-3b`……….`(1)`
Given, `f(-1)+f(2)=0`
`implies (a+(3a-b)-3b)+(4a+2b-6a-3b)=0`
`implies 2a-5b=0`
`implies (b)/(a)=(2)/(5)` ………..`(2)`
Now, product of roots `=(-3b)/(a)=-3((2)/(5))`
since one root...