Question

find the projection of the vector A=i cap+ 2j cap+k cap on the vector b =4i cap - 4j cap+ 7k cap
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Answer 1

Given :-

A = i + 2j + k

B = 4i - 4j + 7k

We are asked to find the projetion of A to B. Hence, we know a formula i.e.,

Projection of A on B = (A • B)/|B|

A • B = (i + 2j + k) • ( 4i - 4j + 7k)

A • B = 4 - 8 + 7

A • B = 3

Again,

|B| = √(4)² +(-4)² + (7)²

|B| = √16 + 16 + 49 = √81 = 9

Putting these both values in the formula.

Projection of A on B = (A • B)/|B|

Projection of A on B = 3/9

Projection of A on B = 1/3 Answer.......