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is correct thanks

question1.

find the vector component of 2i+j-k in the direction of i-3j+2k

basically i use the rule

a=(v*w^)*w^

w^= i-3j+2k / sqrt(14)

thus v=2i+j-k

therefore a=(2i+j-k)*( i-3j+2k / sqrt(14) ) * (i-3j+2k / sqrt(14))

a= [2(1)-3(1)-1(2) /sqrt(14)] * [i-3j+2k / sqrt(14)]

a= -3/sqrt(14)* i-3j+2k / sqrt(14)

thus the vector componentis a=-3/14( i-3j+2k) ???

2. find the parametric equationsof the straightline of intersection of the planes

x-2y+3z=5

3x+y-2z=1

i used gaussian elimination and got the tableu

1 -2 3 | 5

3 1 -2 | 1 R2-3R1

1 -2 3 | 5

0 7 -11| -14

x-2y+3z=5

7y-11z=-14

z=t

sub z=t into 7y-11z=-14

y=11t/7 - 2

sub y=11t/7 - 2 into x-2y+3z=5

x= 5 + 1/7t

therefore are the parametric equations

x= 5 + 1/7t

y=11t/7 - 2

z=t

??

thanks all