HSC X Task 1

Question 1

Answer 1

Question 1

Answer 1

Question 2

the shortest distance of a point to a line is

Answer 2

the perpendicular distance from the point to the line

Question 3

Answer 3

Question 4

projecting a onto b

Answer 4

Question 5

proj length is just

Answer 5

the scalar projection x the magnitude of the vector

Question 6

how to find the unit vector in that direction?

Answer 6

divide that vector X with the (scalar) magnitude of vector X

Question 7

Answer 7

Question 8

The Binomial Theorem

Answer 8

Question 9

n choose 0 is equal to

Answer 9

n choose n which is equal to 1

Question 10

n choose 1 is equal to

Answer 10

n choose (n - 1) which is equal to n

Question 11

n choose 2 is equal to

Answer 11

n choose (n - 2) = 0.5n(n-1)

Question 12

some particular values for n choose r

Answer 12

Question 13

dot product 2 diff formulas

Answer 13

Question 14

projection of u on x
and its length

Answer 14

Question 15

identities in pascal’s triangle

Answer 15

Question 16

prove

Question 17

parallel vectors…

Answer 17

are scalar multiples of each other

Question 18

collinear vectors…

Answer 18

are parallel (scalar multiples) and share a point

Question 19

perpendicular vectors

Answer 19

their dot product is 0