AIEEE 2007 | 3D Geometry Question 297 | Mathematics

If a line makes an angle of $$\pi /4$$ with the positive directions of each of $$x$$-axis and $$y$$-axis, then the angle that the line makes with the positive direction of the $$z$$-axis is :

$${\pi \over 4}$$

$${\pi \over 2}$$

$${\pi \over 6}$$

$${\pi \over 3}$$

AIEEE 2007

MCQ (Single Correct Answer)

-1

Out of Syllabus

If $$(2,3,5)$$ is one end of a diameter of the sphere $${x^2} + {y^2} + {z^2} - 6x - 12y - 2z + 20 = 0,$$ then the coordinates of the other end of the diameter are

$$(4, 3, 5)$$

$$(4, 3, -3)$$

$$(4, 9, -3)$$

$$(4, -3, 3)$$

AIEEE 2007

MCQ (Single Correct Answer)

-1

Let $$L$$ be the line of intersection of the planes $$2x+3y+z=1$$ and $$x+3y+2z=2.$$ If $$L$$ makes an angle $$\alpha $$ with the positive $$x$$-axis, then cos $$\alpha $$ equals

$$1$$

$${1 \over {\sqrt 2 }}$$

$${1 \over {\sqrt 3 }}$$

$${1 \over 2}$$

AIEEE 2006

MCQ (Single Correct Answer)

-1

Out of Syllabus

The image of the point $$(-1, 3,4)$$ in the plane $$x-2y=0$$ is :

$$\left( { - {{17} \over 3}, - {{19} \over 3},4} \right)$$

$$(15,11,4)$$

$$\left( { - {{17} \over 3}, - {{19} \over 3},1} \right)$$