If `r=i+j+lamda(2i+j+4k)` and `r.(i+2j-k)=3` are the equations of a line and a plane respectively then which of the following is true?

If r=hat(i)+hat(j)+lambda(2hat(i)+hat(j)+4hat(k)) and r*(hat(i)+2hat(j)-hat(k)=3 are equations of a line and a plane respectively, then which of the following is incorrect?

If r=hat(i)+hat(j)+lambda(2hat(i)+hat(j)+4hat(k)) and r*(hat(i)+2hat(j)-hat(k)=3 are equations of a line and a plane respectively, then which of the following is incorrect?

A : The vector equation of the plane passing through the point 2i + 2j - 3k and parallel to the vectors 3i + 3j - 5k, i + 2j + k is r = 2i + 2j - 3k + s(3i + 3j - 5k) + t(i + 2j + k) R : The vector equation of the plane passing through the points a, b, c is r = (1 - s - t) a + sb + tc

Equation of the plane containing the line vec r = i+j + lambda (2i+j+4k) is

Let s_1 = {(i,j, k) ∶ i,j, k ∈ {1,2, … ,10}} , s_2 = {(i,j) ∶ 1 ≤ i s_3 = {(i,j, k, l) ∶ 1 ≤ i s_4 = {(i,j, k, l) ∶ i,j, k and l are distinct elements in {1,2, … ,10}} . If the total number of elements in the set s_r is n_r , r= 1,2,3,4, then which of the following statements is (are) TRUE ?

Equation of the plane passing through the points i+j-2k,2i-j+kandi+2j+k is

If the vector equation of a line is barr=i+j+k+mu(2i-3j-4k) , then the Cartesian equation of the line is

equation of the plane containing the lines (i+2j-k)+s(i+j+3k) is

The cartesian equation of the line passing through the points 2i + j + 3k, -4i + 3j - k is