Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Three-dimensional Geometry

Question:

Match List-I with List-II

List-I

List-II

(A) Equations of line through (5, -4, 6) with direction ratios 3, 7, 2

(I) $\frac{x+3}{5}=\frac{y+7}{-4}=\frac{z+2}{6}$

(B) Equations of line through (3, 7, 2) with direction ratios 5, -4, 6

(II) $\frac{x-3}{5}=\frac{y-7}{-4}=\frac{z-2}{6}$

(C) Equations of line through (-5, 4, -6) with direction ratios 3, 7, 2

(III) $\frac{x-5}{3}=\frac{y+4}{7}=\frac{z-6}{2}$

(D) Equations of line through (-3, -7, -2) with direction ratios 5, -4, 6

(IV) $\frac{x+5}{3}=\frac{y-4}{7}=\frac{z+6}{2}$

Choose the correct answer from the options given below:

Options:

(A)-(III), (B)-(II), (C)-(IV), (D)-(I)

(A)-(III), (B)-(II), (C)-(I), (D)-(IV)

(A)-(IV), (B)-(I), (C)-(III), (D)-(II)

(A)-(I), (B)-(IV), (C)-(II), (D)-(III)

Correct Answer:

(A)-(III), (B)-(II), (C)-(IV), (D)-(I)

Explanation:

The correct answer is Option (1) → (A)-(III), (B)-(II), (C)-(IV), (D)-(I)

List-I

List-II

(A) Equations of line through (5, -4, 6) with direction ratios 3, 7, 2

(III) $\frac{x-5}{3}=\frac{y+4}{7}=\frac{z-6}{2}$

(B) Equations of line through (3, 7, 2) with direction ratios 5, -4, 6

(II) $\frac{x-3}{5}=\frac{y-7}{-4}=\frac{z-2}{6}$

(C) Equations of line through (-5, 4, -6) with direction ratios 3, 7, 2

(IV) $\frac{x+5}{3}=\frac{y-4}{7}=\frac{z+6}{2}$

(D) Equations of line through (-3, -7, -2) with direction ratios 5, -4, 6

(I) $\frac{x+3}{5}=\frac{y+7}{-4}=\frac{z+2}{6}$

Match by reading symmetric form $(x-x_0)/a=(y-y_0)/b=(z-z_0)/c$ so point is $(x_0,y_0,z_0)$ and direction ratios are $(a,b,c)$.

(I) $\frac{x+3}{5}=\frac{y+7}{-4}=\frac{z+2}{6}\Rightarrow$ point $(-3,-7,-2)$, direction ratios $(5,-4,6)$.

(II) $\frac{x-3}{5}=\frac{y-7}{-4}=\frac{z-2}{6}\Rightarrow$ point $(3,7,2)$, direction ratios $(5,-4,6)$.

(III) $\frac{x-5}{3}=\frac{y+4}{7}=\frac{z-6}{2}\Rightarrow$ point $(5,-4,6)$, direction ratios $(3,7,2)$.

(IV) $\frac{x+5}{3}=\frac{y-4}{7}=\frac{z+6}{2}\Rightarrow$ point $(-5,4,-6)$, direction ratios $(3,7,2)$.