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# Express the vector a = ( 5i - 2j + 5k ) as sum of two vectors such that one is parallel to the vector b = ( 3i + k ) and the other is perpendicular to vector b.

9 years ago

Hi Chanchal,

Now let a = x(3i+k) + (pi - 2j + qk)

The second Vector must be perpendicular to b

So 3p+q=0----------------(1)

And also 3x+p = 5,

x+q = 5.... or 3x+3q = 15

Subtracting, 3q-p = 10..... solve this with (1)

You will get q=3, p = -1.

And x = 2

Substitute the values, and get the vectors.

Best Regards,

8 years ago

hi

express the vector a=(5i-2j+5k) as the sum of two vectors suchthat one is paralll to the vector b=(3i+k)

and the other is perpendicular to vector b

9 months ago
Dear Student,

Now let a = x(3i+k) + (pi - 2j + qk)
The second Vector must be perpendicular to b
So 3p+q=0----------------(1)
And also 3x+p = 5,
x+q = 5.... or 3x+3q = 15
Subtracting, 3q-p = 10..... solve this with (1)
You will get q=3, p = -1.
And x = 2
Substitute the values, and get the vectors.

Thanks and Regards