Question

- 12. If Ă = (i+2j + k), B = (2i + 3k ) and C = (-2i + 4 K ) then magnitude of vector (A + B - C ) is
a) √20
b) √29
c) √65
d) √69​

Answer 1

Answer:

2i+3j−3k

C

2i−j+5k

Any vector in the plane b and c is

r=b+λc=(i+2j+k)+λ(i+j−2k)

=(1+λ)i+(2+λ)j+(−1−2λ)k

Projection of r on a is =

∣a∣

r.a

=

4+1+1

2(1+λ)−(2+λ)−(1+2λ)

=

6

−λ−1

∴

6

−λ−1

=±

3

2

⇒−λ−1=±2⇒λ=−3,1

Hence r=−2i−j+5k and r=2i+3j−3k

Answer 2

Answer:

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