Vectors 1 Question 4

4. Let a=i^+j^+2k^,b=b1i^+b2j^+2k^ and c=5i^+j^+2k^ be three vectors such that the projection vector of b on a is a. If a+b is perpendicular to c, then |b| is equal to

(a) 6

(b) 4

(c) 22

(d) 32

Show Answer

Answer:

Correct Answer: 4. (b)

Solution:

  1. According to given information, we have the following figure.

Clearly, projection of b on a=ba|a|

=(b1i^+b2j^+2k^)(i^+j^+2k^)12+12+(2)2=b1+b2+24=b1+b2+22

But projection of b on a=|a|

b1+b2+22=12+12+(2)2

b1+b2+22=2b1+b2=2

Now, a+b=(i^+j^+2k^)+(b1i^+b2j^+2k^)

=(b1+1)i^+(b2+1)j^+22k^

(a+b)c, therefore (a+b)c=0

(b1+1)i^+(b2+1)j^+22k^(5i^+j^+2k^)=0

5(b1+1)+1(b2+1)+22(2)=0

5b1+b2=10

From Eqs. (i) and (ii), b1=3 and b2=5

b=3i^+5j^+2k^

|b|=(3)2+(5)2+(2)2=36=6



NCERT Chapter Video Solution

Dual Pane