Question

Find the projection and magnitude of the given vector

Answer 1

HELLO DEAR,

vector a = 4i + j + 3k,

vector b = i - j + k

the projection of  vector a on vector b = $\sf{{(\vec{a} .\vec{b})\over|\vec{b}|}}$

(vector a . vector b) = (4*1) + {1 * (-1)} + (3 * 1)

= 4 - 1 + 3

(vector a . vector b) = 6

AND, magnitude of vector b = √{1 + 1 + 1}

= √3

so, the projection of  vector a on vector b = $\sf{{(\vec{a}.\vec{b})\over|\vec{b}|}}$ = 6/√3

= 6√3/3

= 2√3

I HOPE ITS HELP YOU DEAR,

THANKS

Answer 2

Dear Student:

a=4i+j+3k

b=i-j+k

Vector Projection of a on b is given as,

See the attachment: