A line passes through the point (2,1,-3) and is parallel to the vector `(hat(i) -2hat(j) +2hat(k))` . Find the equations of the line in vector and Cartesian forms .
Answered Feb 05, 2023
Correct Answer - `vec(r )=(2hat(i)-hat(j)-3hat(k)) +lambda (hat(i) -2hat(j)+3hat(k)) ,(x-2)/(1)=(y-1)/(-2)=(z+3)/(3)`
Correct Answer - (i) 9 (ii) 8 (iii) -7
Correct Answer - `lambda=1`
Correct Answer - `vec(r ) =(2hat(i) +hat(j) -5hat(k)) +lambda(hat(i) +3hat(j)-hat(k)) ,(x-2)/(1)=(y-1)/(3)=(z+5)/(-1)`
Correct Answer - `vec(r )=(2hat(i) -hat(j) +4hat(k)) +lambda(hat(i)-hat(j)-2hat(k)) ,(x-2)/(1)=(y+1)/(1)=(z-4)/(-2)`
Correct Answer - `cos^(-1) .((8sqrt(3))/(15))`
Correct Answer - `(10)/(sqrt(59))` units
Correct Answer - `(3sqrt(19))/(19)` units
Correct Answer - `(3sqrt(2))/(2)` units
Correct Answer - `vec(d)=7(hat(i)-hat(j)-hat(k))`
Correct answer is (a) We know that propagation wave vector ∵ \(\vec{E} = \hat{k}\) \(\vec{B} = 2\hat{i} - 2\hat{j}\) \(\vec{C} = \vec{E} \times \vec{B}\) \(\vec{C} = \begin{vmatrix} \hat{i} & \hat{j} & \hat{k} \\ 0 & 0 & 1...
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