Question

The value of 'p' for which the vectors 2i - j +k, 3i + pj +5k ( i, j, k are unit vectors) are
coplanar is /????

Answer 1

if two vectors are non -colinear vectors ,then they must be coplanar . e.g they must be lies in same plane .

now,
Let
( 2i - j + K) and ( 3i + Pj + 5k ) are coplanar vectors so, both are also non- colinear vector .

hence,

x( 2i - j + k) + y ( 3i +Pj +5k) = 0

(2x + 3y)i + ( -x + Py)j + ( x + 5y)K = 0

2x + 3y = 0
x + 5y = 0
-x + Py = 0

(2x + 3y) = ( x + 5y)

x = 2y

put in ( -x + Py) =0

-2y + Py = 0

y( -2 + P) = 0

P -2 = 0

P = 2

hence, P =2

Answer 2

Step-by-step explanation:

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