3D Geometry

Question 1

What is the equation of vector passing through vector r1 and parallel to vector m?

Answer 1

Equation of vector passing through position vector r1 and parallel to m is given by r=r1+λm

Question 2

What is the equation of vector in cartesian form?

Answer 2

Equation of vector in cartesian form is given by: point (x1,y1,z1)
x-x1/a=y-y1/b=z-z1/c

Question 3

What is the vector equation of a line passing through two points for position vector r1 and r2 ?

Answer 3

The vector equation of a line passing through 2 points for position vectors r1 and r2 is given by: r=(1-λ)r1+λr2

Question 4

What is the vector equation in cartesian form for line passing through points (x1,y1,z1) and (x2,y2,z2)

Answer 4

The vector equation in cartesian form for line passing through points (x1,y1,z1) and (x2,y2,z2) is : x-x1/x2-x1=y-y1/y2-y1=z-z1/z2-z1

Question 5

What is the angle between two vector lines r=r1+λm1 and r=r2+λm2 ?

Answer 5

cos ∅= m1 . m2/ | m1 | | m2 |

Question 6

What is the angle between two vectors if their equation is given in their respective cartesian forms?

Answer 6

cos ∅= a1a2 + b1b2 + c1c2/ ((√a1²+b1²+c1²) (√a2²+b2²+c2²))

Question 7

What is the shortest distance between two vectors given by equations r=r1+λu and r=r2+μv ?

Answer 7

The shortest distance between two vectors is given by:

d= (r2-r1) . (u x v)/ | u x v |

Question 8

What is the shortest distance between two vectors whose equations are given in their respective cartesian forms?

Answer 8

Since its written in determinant form, hence please look into the copy or tablet and write it down

Question 9

In cross product, what is i x j and j x i?

j x k and k x j? k x i and i x k?

Answer 9

In cross product, i x j = k and j x i = -k
j x k= i and k x j = -i
k x i = j and i x k = -j

Question 10

If vectors a and b represent the sides of any triangle, then how is the area of triangle given by?

Answer 10

Area of Triangle is given by : 1/2| a x b |

Question 11

If vectors a and b represent the diagonals of a quadrilateral then how is the area of the quadrilateral given by?

Answer 11

Area of quadrilateral is given by: 1/2 | a x b |

same as Triangles except sides its diagonals

Question 12

Go through Scalar Triple product in the tablet app

Answer 12

Go through Scalar Triple product in the tablet app