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Component of 3i+4j along i+j. Options are (a) ½ (i+j) (b) 3/2(j-i) (c) 5/2(j-i) (d) 7/2(i+j)

Component of  3i+4j along i+j.

Options are


(a) ½ (i+j)

(b) 3/2(j-i)

(c) 5/2(j-i)

(d) 7/2(i+j)

Grade:11

7 Answers

Sagar Gupta
39 Points
7 years ago
Let A= 3i+4j and a(cap) be the unit vector along i+j .First find the unit vector of I+j so it will be I+j/|i+j| = 1/√2 (i+j) .Now find the Magnitude of component of 3i+4j by dot product of 3i+4j with I+j/√2 so it will be 7/√2So We got the Magnitude of Component of the vectorNow Component of 3i+2j along I+j= Magnitude of 3i+4j × unit vector of I+j=7/√2(i+j) D is your Answer.
harveer singh
19 Points
6 years ago
Let A= 3i+4j and a(cap) be the unit vector along i+j .First find the unit vector of I+j so it will be I+j/|i+j| = 1/√2 (i+j) .Now find the Magnitude of component of 3i+4j by dot product of 3i+4j with I+j/√2 so it will be 7/√2So We got the Magnitude of Component of the vectorNow Component of 3i+2j along I+j= Magnitude of 3i+4j × unit vector of I+j=7/2(i+j) D is your Answer.
abhishek
19 Points
6 years ago
3i+4j is the componentFirstly find its unit vector ...it will be 1/√2Then find magnitude of vector that will be 7..And we will already have the value of I +j is 1/√2 so applied and in component formula then u will got the answer 7/√2(I+j)
Samir
13 Points
6 years ago
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Ankush
13 Points
5 years ago
3i+4j is the componentFirstly find its unit vector ...it will be 1/√2Then find magnitude of vector that will be 7..And we will already have the value of I +j is 1/√2 so applied and in component formula then u will got the answer 7/√2(I+j) so answer is D
Bhavesh Jha
13 Points
5 years ago
Let Ā= 3î+4j and b=î+j
Component of a along b is given by (a.b/|b|)  b^ so the answer by using the formula is (3+4)/root 2 b
Hence we get 7/root 2 ( i+j).
Kushagra Madhukar
askIITians Faculty 628 Points
3 years ago
Dear student,
Please find the solution to your problem.
 
Let A = 3i + 4j and a(cap) be the unit vector along i+j .
Unit vector along i + j, B =  i + j/|i + j| = 1/√2 (i + j) .
Magnitude of Component of 3i + 4j along the unit vector B =  A.B = 7/√2
Hence, Component of 3i + 2j along i + j = Magnitude of 3i + 4j × unit vector B =7/√2 (i + j)
Hence, D is your Answer.
 
Thanks and regards,
Kushagra

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