99 Percentile Qs Bank for JEE MainMathematicsVector Algebra

If a =4 i +6 j , b =3 j +4 k and c . is the projection vector of a on b , then c and | c | respectively are

Options

A18 25 b, 18 5
B18 5 b, 18
C25 18 b, 18 5
D5 18 b, 5 18

Correct answer

A. 18 25 b, 18 5

Step-by-step solution

a =4 i +6 j , b =3 j +4 k c is the projection vector of a on b aligned & c = a b | b | = (4 i +6 j ) (3 j +4 k ) 3^2+4^2 & c = 18 5 j | c |= 18 5 aligned Now, | b |=5 Then, |c| |b| = 18 25 | c |= 18 25 | b |=0 | c |= 18 25 5= 18 5 c and b are collinear vectors. c= 18 25 b

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