NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra Ex 10.4

In this chapter, we provide NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra Ex 10.4 for English medium students, Which will very helpful for every student in their exams. Students can download the latest NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra Ex 10.4 pdf, free NCERT solutions for Class 12 Maths Chapter 10 Vector Algebra Ex 10.4 book pdf download.

BoardCBSE
TextbookNCERT
ClassClass 12
SubjectMaths
ChapterChapter 10
Chapter NameVector Algebra
ExerciseEx 10.4
Number of Questions Solved12
CategoryNCERT Solutions

NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra Ex 10.4

Ex 10.4 Class 12 Maths Question 1.
Find left| overrightarrow { a } times overrightarrow { b } right| ,ifquad overrightarrow { a } =hat { i } -7hat { j } +7hat { k } quad andquad overrightarrow { b } =3hat { i } -2hat { j } +2hat { k }
Solution:
Given
overrightarrow { a } =hat { i } -7hat { j } +7hat { k } quad andquad overrightarrow { b } =3hat { i } -2hat { j } +2hat { k }
NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra 1

NCERT Maths Class 12 Chapter 10

Ex 10.4 Class 12 Maths Question 2.
Find a unit vector perpendicular to each of the vector overrightarrow { a } +overrightarrow { b } quad andquad overrightarrow { a } -overrightarrow { b } , where overrightarrow { a } =3hat { i } +2hat { j } +2hat { k } quad andquad overrightarrow { b } =hat { i } +2hat { j } -2hat { k }
Solution:
we have
overrightarrow { a } =3hat { i } +2hat { j } +2hat { k } quad andquad overrightarrow { b } =hat { i } +2hat { j } -2hat { k }
NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra 2
NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra 2.1

Ex 10.4 Class 12 Maths Question 3.
If a unit vector overrightarrow { a } makes angle frac { pi }{ 3 } withquad hat { i } ,frac { pi }{ 4 } withquad hat { j } and an acute angle θ with overrightarrow { k } ,then find θ and hence the components of overrightarrow { a } .
Solution:
Letquad overrightarrow { a } ={ a }_{ 1 }hat { i } +{ a }_{ 2 }hat { j } +{ a }_{ 3 }hat { k } suchquad thatquad left| overrightarrow { a } right| =1
NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra 3

Ex 10.4 Class 12 Maths Question 4.
Show that left( overrightarrow { a } -overrightarrow { b } right) times left( overrightarrow { a } +overrightarrow { b } right) =2left( overrightarrow { a } times overrightarrow { b } right)
Solution:
LHS = left( overrightarrow { a } -overrightarrow { b } right) times left( overrightarrow { a } +overrightarrow { b } right)
vedantu class 12 maths Chapter 10 Vector Algebra 4

Ex 10.4 Class 12 Maths Question 5.
Find λ and μ if
left( 2hat { i } +6hat { j } +27hat { k } right) times left( hat { i } +lambda hat { j } +mu hat { k } right) =0
Solution:
left( 2hat { i } +6hat { j } +27hat { k } right) times left( hat { i } +lambda hat { j } +mu hat { k } right) =0
NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra 5

Ex 10.4 Class 12 Maths Question 6.
Given that overrightarrow { a } .overrightarrow { b } =0quad andquad overrightarrow { a } times overrightarrow { b } =0. What can you conclude about the vectors overrightarrow { a } ,overrightarrow { b } ?
Solution:
overrightarrow { a } .overrightarrow { b } =0quad andquad overrightarrow { a } times overrightarrow { b } =0
NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra 6

Ex 10.4 Class 12 Maths Question 7.
Let the vectors overrightarrow { a } ,overrightarrow { b } ,overrightarrow { c } are given { a }_{ 1 }hat { i } +{ a }_{ 2 }hat { j } +{ a }_{ 3 }hat { k } ,{ b }_{ 1 }hat { i } +{ b }_{ 2 }hat { j } +{ b }_{ 3 }hat { k } ,{ c }_{ 1 }hat { i } +{ c }_{ 2 }hat { j } +{ c }_{ 3 }hat { k } . Then show that overrightarrow { a } times left( overrightarrow { b } +overrightarrow { c } right) =overrightarrow { a } times overrightarrow { b } +overrightarrow { a } times overrightarrow { c }
Solution:
Given
overrightarrow { a } ,overrightarrow { b } ,overrightarrow { c } are given { a }_{ 1 }hat { i } +{ a }_{ 2 }hat { j } +{ a }_{ 3 }hat { k } ,{ b }_{ 1 }hat { i } +{ b }_{ 2 }hat { j } +{ b }_{ 3 }hat { k } ,{ c }_{ 1 }hat { i } +{ c }_{ 2 }hat { j } +{ c }_{ 3 }hat { k }
vedantu class 12 maths Chapter 10 Vector Algebra 7
NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra 7.1

Ex 10.4 Class 12 Maths Question 8.
If either overrightarrow { a } =0quad orquad overrightarrow { b } =0quad thenquad hat { a } times hat { b } =0.Is the
converse true? Justify your answer with an example.
Solution:
overrightarrow { a } =0Rightarrow left| overrightarrow { a } right| =0
NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra 8

Ex 10.4 Class 12 Maths Question 9.
Find the area of the triangle with vertices A (1,1,2), B (2,3,5) and C (1,5,5).
Solution:
A (1,1,2), B (2,3,5) and C (1,5,5).
NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra 9
NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra 9.1

Ex 10.4 Class 12 Maths Question 10.
Find the area of the parallelogram whose adjacent sides are determined by the vectors overrightarrow { a } =hat { i } -hat { j } +3hat { k } ,overrightarrow { b } =2hat { i } -7hat { j } +hat { k }
Solution:
We have overrightarrow { a } =hat { i } -hat { j } +3hat { k } ,overrightarrow { b } =2hat { i } -7hat { j } +hat { k }
vedantu class 12 maths Chapter 10 Vector Algebra 10

Ex 10.4 Class 12 Maths Question 11.
Let the vectorsoverrightarrow { a } ,overrightarrow { b } such that left| overrightarrow { a } right| =3,left| overrightarrow { b } right| =frac { sqrt { 2 } }{ 3 } then overrightarrow { a } times overrightarrow { b } is a unit vector if the angle between overrightarrow { a } ,overrightarrow { b } is
(a) frac { pi }{ 6 }
(b) frac { pi }{ 4 }
(c) frac { pi }{ 3 }
(d) frac { pi }{ 2 }
Solution:
Given
left| overrightarrow { a } times overrightarrow { b } right| =1
left| overrightarrow { a } right| =3,left| overrightarrow { b } right| =frac { sqrt { 2 } }{ 3 }
NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra 11

Ex 10.4 Class 12 Maths Question 12.
Area of a rectangles having vertices
Aleft( -hat { i } +frac { 1 }{ 2 } hat { j } +4hat { k } right) ,Bleft( hat { i } +frac { 1 }{ 2 } hat { j } +4hat { k } right) ,
Cleft( hat { i } -frac { 1 }{ 2 } hat { j } +4hat { k } right) ,Dleft( -hat { i } -frac { 1 }{ 2 } hat { j } +4hat { k } right) ,
(a) frac { 1 }{ 2 } sq units
(b) 1sq.units
(c) 2sq.units
(d) 4sq.units
Solution:
overrightarrow { OA } =left( -hat { i } +frac { 1 }{ 2 } hat { j } +4hat { k } right)
overrightarrow { OB } =left( hat { i } +frac { 1 }{ 2 } hat { j } +4hat { k } right)
NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra 12

All Chapter NCERT Solutions For Class12 Maths

—————————————————————————–

All Subject NCERT Solutions For Class12

*************************************************

Remark:

I think you got complete solutions for this chapter. If You have any queries regarding this chapter, please comment on the below section our subject teacher will answer you. We tried our best to give complete solutions so you got good marks in your exam.

If these solutions have helped you, you can also share Careerkundali.in to your friends.

Best of Luck!!

Leave a Comment

Your email address will not be published. Required fields are marked *