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NCERT Solutions Class 12 Maths Chapter-10 ( Vector Algebra) Exercise 10.4

NCERT Solutions Class 12 Maths Chapter-10 (Vector Algebra) Exercise 10.4

NCERT Solutions Class 12 Maths from class 12th Students will get the answers of Chapter-10 (Vector Algebra)Exercise 10.4 This chapter will help you to learn the basics and you should expect at least one question in your exam from this chapter.
We have given the answers of all the questions of NCERT Board Mathematics Textbook in very easy language, which will be very easy for the students to understand and remember so that you can pass with good marks in your examination.
NCERT Solutions Class 12 Maths Chapter-10 ( Vector Algebra) Exercise 10.4
Exercise 10.4

Q1. 

Answer. a=i^7j^+7k^ and b=3i^2j^+2k^ a×b=|i^j^k^177322| 

Q2. 

Answer.  We have, a=3i^+2j^+2k^ and b=i^+2j^2k^a+b=4i^+4j^,ab=2i^+4k^ (a+b)×(ab)=|i^j^k^440204|=i^(16)j^(16)+k^(8)=16i^16j^8k^ (a+b)×(ab)=162+(16)2+(8)2=22×82+22×82+82=822+22+1=89=8×3=24 

Q3.  If a unit vector a makes an angles 3 with i,π4 with ȷ^ and an acute angle θ with k^ , then  find θ and hence, the compounds of a . 

Answer.  Let unit vector a have (a1,a2,a3) components. a¯=a1i^+a2j^+a3k^ since a is a unit vector, |a|=1 cosπ3=a1|a|12=a1cosπ4=a2|a|12=a2 Also, cosθ=a3|a|  Now |a|=1a12+a22+a32=1(12)2+(12)2+cos2θ=134+cos2θ=134+cos2θ=1 34+cos2θ=1cos2θ=134=14cosθ=12θ=π3a3=cosπ3=12 

Q4. 

Answer. 

Q5. Find λ and μ if 

Answer. (2i^+6j^+27k^)×(i^+λj^+μk^)=0|j^k^26271λμ|=0i^+0j^+0k^i^(6μ27λ)j^(2μ27)+k^(2λ6)=0i^+0j^+0k^ 

Q6. Given that 

Answer. ab=0 Then,  (i) Either |a|=0 or |b|=0 or ab( in case a and b are non-zero )a×b=0 (ii) Either |a¯|=0 or |=0, or ab( in case a and b are non-zero ) 

Q7. 

Answer.  we have, a=a1i^+a2j^+a3k^,b=b1i^+b2j^+b3k^,c=c1i^+c2j^+c3k^(b+c)=(b1+c1)i^+(b2+c2)j^+(b3+c3)k^