JEE Advanced 2020 Full Test 4 Paper 2

Let

→

r

=λ

→

b

+µ

→

c

and

→

c

=±(xi+yj). Since

→

c

and

→

b

are perpendicular, we have
we have 4x+3y=0‌‌⇒‌‌

→

c

=±x(i−‌

4

3

j)
±1= proj. of

→

r

on

→

b

=‌

→ r ⋅ → b

| → b |

=‌

(λ → b +µ → c ) → b

| → b |

=‌

λ → b ⋅ → b

| → b |

[∵

→

b

.

→

c

=0]
=λ|

→

b

|=5λ. Hence λ=±‌

1

5

Also, ±2= proj. of

→

r

on

→

c

=‌

→ r ⋅ → c

| → c |

(λ → b +µ → c ) → c

| → c |

=µ|

→

c

|=‌

5

3

µx
Thus, µx=±‌

6

5

. Therefore

→

r

=‌

1

5

(4i+3j)+‌

6

5

(i−‌

4

3

j)=±(2i−j)

→

r

=‌

1

5

(4i+3j)−‌

6

5

(i−‌

4

3

j)=±(−‌

2

3

i+‌

11

5

j)
Thus there are four such vectors s

4

∑

i=1

|

→

r

i|2=2|2i−j|2+2∣−‌

2

5

i+‌

11

5

j2=20