Solve `r timesb=a`, where a and b are given vectors such that `a*b=0`.

Solve: vecrxxvecb=veca, where veca and vecb are given vectors such that veca.vecb=0 .

Solve for vec x,vecx xx vec b=veca , where veca,vecb are two given vectors such that veca is perpendicular to vecb .

Let a, b and c be non-zero vectors and |a|=1 and r is a non-zero vector such that r times a=b and r*a=1 , then

Let R be a relation defined by R = {(a, b) : a ge b }, where a and b are real numbers, then R is

Let a and b be given non-zero and non-collinear vectors, such that ctimesa=b-c . Express c in terms for a, b and aXb.

If vec a and vec b are two given vectors and k is any scalar, then find the vector vec r satisfying vec rxx vec a+k vec r= vec b .

The radius vector of a point depends on time t, as r = c t +(b t^(2))/(2) where c and b are constant vectors. Find the modulus of velocity and acceleration at any time t.

The xz plane separates two media A and B with refractive indices mu_(1) & mu_(2) respectively. A ray of light travels from A to B . Its directions in the two media are given by the unut vectors, vec(r)_(A)=a hat i+ b hat j & vec(r)_(B) alpha hat i + beta hat j respectively where hat i & hat j are unit vectors in the x & y directions. Then :

The xz plane separates two media A and B with refractive indices mu_(1) & mu_(2) respectively. A ray of light travels from A to B . Its directions in the two media are given by the unit vectors, vec(r)_(A)=a hat i+ b hat j & vec(r)_(B)= alpha hat i + beta hat j respectively where hat i & hat j are unit vectors in the x & y directions. Then :

Let alpha = (lambda-2) a + b and beta =(4lambda -2)a + 3b be two given vectors where vectors a and b are non-collinear. The value of lambda for which vectors alpha and beta are collinear, is.