The two points on the line `x +y =4 `that at a unit perpendicular distance from the line lie `4x +3y =10` are `(a_1, b_1)` and `(a_2, b_2)`, then `a_1+ b_1+a_2+ b_2 `

The two points on the line x+y=4 that lies at a unit perpendicular distance from the line 4x+3y=10 are (a_(1), b_(1)) and (a_(2), b_(2)) then a_(1)+b_(1)+a_(2)+b_(2) is equal to

If the equation of the locus of a point equidistant from the points (a_1,b_1) and (a_2,b_2) is (a_1-a_2)x+(b_2+b_2)y+c=0 , then the value of C is

If the points (a_1, b_1),\ \ (a_2, b_2) and (a_1+a_2,\ b_1+b_2) are collinear, show that a_1b_2=a_2b_1 .

Let vec a=a_1 hat i+a_2 hat j+a_2 hat k , vec b=b_1 hat i+a_2 hat j+b_2 hat k ,a n d vec c=c_1 hat i+c_2 hat j+c_2 hat k , be three non-zero vectors such that vec c is a unit vector perpendicular to both vectors vec aa n d vec b . If the angle between aa n db is pi//6, then |a_1a_2a_3b_1b_2b_3c_1c_2c_3|^2 is equal to 0 1 1/4(a1 2+a2 2+a3 2)(b1 2+b2 2+b3 2) 3/4(a1 2+a2 2+a3 2)(b1 2+b2 2+b3 2)(c1 2+c2 2+c3 2)

Let vec a = a_1 hat i + a_2 hat j+ a_3 hat k;vec b = b_1 hat i+ b_2 hat j+ b_3 hat k ; vec c= c_1hat i + c_2 hat j+ c_3 hat k be three non-zero vectors such that vec c is a unit vector perpendicular to both vec a & vec b. If the angle between vec a and vec b is pi/6 , then |(a_1,b_1,c_1),(a_2,b_2,c_2),(a_3,b_3,c_3)|^2=

In direct proportion a_1/b_1 = a_2/b_2

The capacitance of the capacitors of plate areas A_1 and A_2(A_1 lt A_2) at a distance d is

a_1, a_2, a_3, in R-{0} and a_1+a_2cos2x+a_3sin^2x=0fora l lx in R , then (a)vector vec a=a_1 hat i+a_2 hat j+a_3 hat ka n d vec b=4 hat i+2 hat j+ hat k are perpendicular to each other (b)vector vec a=a_1 hat i+a_2 hat j+a_3 hat ka n d vec b=- hat i+ hat j+2 hat k are parallel to each other (c)vector vec a=a_1 hat i+a_2 hat j+a_3 hat k is of lengthsqrt(6) units, then one of the ordered triple (a_1, a_2, a_3)=(1,-1,-2) (d)are perpendicular to each other if 2a_1+3a_2+6a_3=26 ,t h e n|a_1 hat i+a_2 hat j+a_3 hat k|i s2sqrt(6)

If the tangent and normal to xy=c^2 at a given point on it cut off intercepts a_1, a_2 on one axis and b_1, b_2 on the other axis, then a_1 a_2 + b_1 b_2 = (A) -1 (B) 1 (C) 0 (D) a_1 a_2 b_1 b_2

If a_mhati+b_mhatj+c_mhatk m=1,2,3 are pairwise perpendicular unit vectors then |[a_1,b_1,c_1] , [a_2,b_2,c_2] , [a_3,b_3,c_3]| is equal to