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NCERT Solutions Class 12 Maths (Vector Algebra) Miscellaneous Exercise

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

NCERT Solutions Class 12 Maths from class 12th Students will get the answers of Chapter-10 (Vector Algebra)Miscellaneous Exercise 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.
Solutions Class 12 Maths (Vector Algebra) Miscellaneous Exercise


Q1. Write down a unit vector in KY-plane, making an angle of 30 with the positive direction of x-axis.

Answer.  If r is a unit vector in the XY-plane, then r=cosθi^+sinθj^ Here, θ is the angle made by the unit vector with the positive direction of the x -axis.  Therefore, for θ=30: 

Q2. 

Answer.  The vector joining the points (x1,y1,z1) and Q(x2,y2,z2) can be obtained by PQ¯= Position vector of Q Position vector of P =(x2x1)i^+(y2y1)j^+(z2z1)k^|PQ|=(x2x1)2+(y2y1)2+(z2z1)2 

Q3. A girl walks 4 km towards west, then she walks 3 km in a direction 30east of north and stops. Determine the girl's displacement from her initial point of departure.

Answer. Let O and B be the initial and final positions of the girl respectively. Then, the girl's position can be shown as: Solutions Class 12 Maths Chapter-10 (Vector Algebra) Miscellaneous Exercise OA=4i^AB=i^|AB|cos60+j^|AB|sin60 =i^3×12+j^3×32=32i^+332j^ OB=OA+AB=(4i^)+(32i^+332j^)=(4+32)i^+332j^=(8+32)i^+332j^=52i^+3323^ 

Q4. If 

Answer. ΔABC, let CB=a,CA=b, and AB=c(as shown in the following figure) Solutions Class 12 Maths Chapter-10 (Vector Algebra) Miscellaneous Exercise Now, by the triangle law of vector addition we have a=b+c It is clearly known that|a¯|,|b|, and |c| Also, it is known that the sum of the lengths of any two sides of a triangle is greater than the third side. |a¯|<|b|+|c¯| Hence it is not true that 

Q5. Find the value of x x for which x(i^+j^+k^) is a unit vector .

Answer. x(i^+j^+k^) is a unit vector if |x(i^+j^+k^)|=1 

Q6. 

Answer. a=2i^+3j^k^ and b=i^2j^+k^ Let c be the resultant of a and b Then, c=a+b=(2+1)i^+(32)j^+(1+1)k^=3i^+j^ c=a+b=(2+1)i^+(32)j^+(1+1)k^=3i^+j^|c|=32+12=9+1=10c^=c|c|=(3i^+j^)10 

Q7.  If a=i^+j^+k^,b=2i^j^+3k^ and c=i^2j^+k^, find a unit vector parallel to the  vector 2ab+3c

Answer.  we have, a=i^+j^+k^,b=2i^+3k^ and c=i^2j^+k^2ab+3c=2(i^+j^+k^)(2i^j^+3k^)+3(i^2j^+k^) =2i^+2j^+2k^2i^+j^3k^+3i^6j^+3k^=3i^3j^+2k^|2ab+3c|=32+(3)2+22=9+9+4=22 

Q8. Show that the points A (1, -2, -8), B (5, 0, -2) and C (11, 3, 7) are collinear, and find the ratio in which B divides AC.

Answer.  The given points are A(1,2,8),B(5,0,2), and C(11,3,7) . AB=(51)i^+(0+2)j^+(2+8)k^=4i^+2j^+6k^