vectors

Question 1

scalar triple product

Answer 1

• [a, b, c] = a · (b × c) = b · (c × a) = c · (a × b)

Question 2

vector triple product

Answer 2

A ×(B × C) = (A · C) B − (A ⋅ B)C

Question 3

Foot of perpendicular from a point (x1, y1) to a line ax + by + c = 0

Answer 3

(x - x1)/ a = (y - y1)/b
= - (ax1 + by1 + c)/ (a² + b²)

Question 4

Centroid of a ∆le

Answer 4

• (x1 + x2 + x3) / 3
• (y1 + y2 + y3) / 3

point of intersection of medians

Question 5

Angle b/w lines

Answer 5

cosθ = a.b / |a||b|