Let P and Q be two points in the xy plane on the curve `y=x^(7)+3x^(5)-5x^(3)+2x+5` such that `vec(OP).hat i=lambda` and `vec(OQ).hat i=-lambda` then magnitude of `vec(OP)+vec(OQ)` is

Let P and Q are two points in the xy plane on the curve y = x^(11) - 2x^(7) + 7x^(3) + 11x + 6 such that vec(OP) cdot hati = 5, vec(OQ) cdot hati = -5 , then the magnitude of vec(OP) + vec(OQ) is

If two point P and Q are on the curve y=2^(x+2) , such that vec(OP).hati=-1 and vec(OQ).hati=2 , where hati is a unit vector along the x - axis, then |vec(OQ)-4vec(OP)| is equal to

3.Two points P and Q are lying on the curve y=log_(2)(x+3) in xy plane such that vec (OP) . hat i=1 and , vec OQ*hat j=3 ,then the value of |vec (OQ)-2vec (OP)| is (where,"O" is the origin). 1) sqrt(6) 2) sqrt(7) 3) sqrt(8) 4) sqrt(10)

If P and Q are two given points on the curve y=x+(1)/(x) such that vec OP.hat i=1 and vec OQ*hat i=-1 where i is a unit vector along x - axis then the length of the vector 3vec OP+2vec OQ is (A) sqrt(5) (B) 3sqrt(5)(C)2sqrt(5)(D)5sqrt(5)

If vec(A) = 3 hat(i) - 4 hat(j) and vec(B) = 2 hat(i) + 16 hat(j) then the magnitude and direction of vec(A) + vec(B) will be

It is given that the vectors vec(a)=(2hat(i)-2hat(k)), vec(b)=hat(i)+(lambda +1)hat(j) and vec(c)=(4hat(j)+2hat(k)) are coplanar. Then, the value of lambda is

Let O be the origin. Let vec(OP) = x hati+y hati-hatk and vec(OQ) = -hati+2hatj+3x hatk, x y in R , x gt 0 , be such that |vec(PQ)|=sqrt(20) and the vector vec(OP) is perpendicular to vec(OQ) . If vec(OR)=3hati+zhatj-7hatk, z in R , is coplanar with vec(OP) and vec(OQ) , then the value of x^(2)+y^(2)+z^(2) is equal to :