CUET Mathematics 2026 22nd May Shift 1 PYQs

P is a point on the line segment joining the points (3, 2, -1) and (6, 2, -2) internally. If x coordinate of P is 5, then its z-coordinate is

Which of the following statements are correct?

(A) The angle between the vectors with direction ratios proportional to -3, 5, 4 and 4, 5, 3 is $\dfrac{\pi}{3}$

(B) The direction cosines of Y-axis is 0, 1, 0.

(C) The cartesian equation of a line is $3x-6=2y+1=2z-1$, then its direction ratios are proportional to 2, 2, 3

(D) The vector equation of the line passing through the point $(2,-1,-1)$ and direction ratios 1, 2, 3 is $\vec r=(2\hat i-\hat j-\hat k)+\lambda(\hat i+2\hat j+3\hat k)$

Choose the correct answer from the options given below:

If the lines $\dfrac{x+1}{3}=\dfrac{y+3}{5}=\dfrac{z+\lambda}{7}$ and $\dfrac{x-2}{1}=\dfrac{y-4}{3}=\dfrac{z-6}{5}$ are intersecting , then the value of '$\lambda$' is