Math, asked by surajbhagivant1311, 3 months ago

projection vector of u=(2,3,1) along (1,4,5) is​

Answers

Answered by ritendramarkam1129
1

Answer:

Projections

P. Danziger

1 Components and Projections

✟✟✟

✟✟✟

✟✟✟

✟✟✟✟

✟✟

θ

✟❆ vu

✟✟✟

✟✟✟✟

projvu

Given two vectors u and v, we can ask how far we will go in the direction of v when we travel

along u. The distance we travel in the direction of v, while traversing u is called the component of

u with respect to v and is denoted compvu. The vector parallel to v, with magnitude compvu, in

the direction of v is called the projection of u onto v and is denoted projvu.

So, compvu = ||projvu||

Note projvu is a vector and compvu is a scalar. From the picture compvu = ||u|| cos θ

We wish to find a formula for the projection of u onto v.

Consider u · v = ||u||||v|| cos θ

Thus ||u|| cos θ =

u · v

||v||

So compvu =

u · v

||v||

The unit vector in the same direction as v is given by v

||v||. So

projvu =

u · v

||v||2

v

Example 1

1. Find the projection of u = i + 2j onto v = i + j.

u · v = 1 + 2 = 3, ||v||2 =

2

2

= 2

projvu =

u · v

||v||2

v =

3

2

(i + j) = 3

2

i +

3

2

Step-by-step explanation:

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