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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.

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.

Grade:11

3 Answers

Ashwin Muralidharan IIT Madras
290 Points
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,

Ashwin (IIT Madras).

maninder singh
18 Points
8 years ago

hi

 

chanchal  plz let me know about this question

 

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

Rishi Sharma
askIITians Faculty 646 Points
9 months ago
Dear Student,
Please find below the solution to your problem.

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

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