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If vec(a)=vec(b)+vec(c ), then is it tru...

If `vec(a)=vec(b)+vec(c )`, then is it true that `|vec(a)|=|vec(b)|+|vec(c )|` ? Justify your answer.

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If vec(a)=vec(b)+vec(c ) , then |vec(a)|=|vec(b)+vec(c )| .

vec(a)+vec(b)+vec(c)=vec(0) such that |vec(a)|=3, |vec(b)|=5 and |vec(c)|=7 . What is vec (a). vec(b) + vec(b). vec(c) + vec(c). vec (a) equal to ?

If vec(a)+vec(b)+vec(c )=0 " and" |vec(a)|=3,|vec(b)|=5, |vec(c )|=7 , then find the value of vec(a),vec(b)+vec(b).vec(c )+vec(c ).vec(a) .

If vec(a), vec(b), vec(c ) are three vectors such that vec(a)xx vec(b)=vec(c ), vec(b)xx vec(c )=vec(a) , prove that vec(a), vec(b), vec(c ) are mutually at right angles and |vec(b)|=1, |vec(c )|=|vec(a)| .

If vec(a),vec(b) and vec(c ) are three vectors such that vec(a)+vec(b)+vec(c )=vec(0) and |vec(a)|=2,|vec(b)|=3 and |vec(c )|=5 , then the value of vec(a)*vec(b)+vec(b)*vec(c)+vec(c)*vec(a) is

If the vectors vec(a), vec(b) and vec(c ) satisfy the condition vec(a)+vec(b)+vec(c )=vec(0) and |vec(a)|=3, |vec(b)| =4 and |vec(c )|=5 , then show that vec(a).vec(b)+vec(b).vec(c )+vec(c ). vec(a)=-25 .

Let vec(a), vec(b) and vec(c) be three vectors such that vec(a) + vec(b) + vec(c) = 0 and |vec(a)|=10, |vec(b)|=6 and |vec(c) |=14 . What is vec(a). vec(b) + vec(b).vec(c)+ vec(c). vec(a) . equal to ?

Let three vectors vec(a), vec(b) and vec(c ) be such that vec(a) xx vec(b) = vec(c), vec(b) xx vec(c) = vec(a) and |vec(a)| = 2 . Then which one of the following is not true ?

If vec(a), vec(b) and vec(c ) are mutually perpendicular unit vectors and vec(a)xx vec(b)=vec(c ) , show that vec(b)=vec(c )xx vec(a) and vec(a)=vec(b)xx vec(c ) .

Show that if vec(a)+vec(b), vec(b)+vec(c ), vec(c )+vec(a) are coplanar, then vec(a), vec(b), vec(c ) are also coplanar.

MODERN PUBLICATION-VECTOR ALGEBRA -Miscellaneous Exercise on Chapter 10
  1. Write down a unit vector in XY-plane, making an angle of 30 with th...

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  2. Find the scalar components and magnitude of the vector joining the po...

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  3. A girl walks 4 km towards west, then she walks 3 km in a direction 30...

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  4. If vec(a)=vec(b)+vec(c ), then is it true that |vec(a)|=|vec(b)|+|vec(...

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

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  6. Find a vector of magnitude 5 units, and parallel to the resultant of ...

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  7. If -> a= hat i+ hat j+ hat k , -> b=2 hat i- hat j+3 hat k and -...

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  8. Show that the points A(1, -2, -8), B(5, 0, -2) and C(11, 3, 7) are col...

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  9. Find the position vector of a point R which divides the line joinin...

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  10. The two adjacent sides of a parallelogram are 2 hat i-4 hat j+5 hat k ...

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  11. Show that the direction cosines of a vector equally inclined to the a...

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  12. Let -> a= hat i+4 hat j+2 hat k , -> b=3 hat i-2 hat j+7 hat k and...

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  13. The scalar product of the vector hat i+ hat j+ hat kwith a unit vect...

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  14. If vec a , vec b , vec c are mutually perpenedicular vectors of eq...

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  15. Prove that ( -> a+ -> b)dot( -> a+ -> c)| -> a|^2+| -> b|^2 , if and o...

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  16. If theta is the angle between two vectors vec a\ a n d\ vec b ,\ t h...

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  17. If vec a\ a n d\ vec b be two unit vectors and theta is the angle be...

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  18. Write the value of hat(i).(hat(j)xxhat(k))+hat(j).(hat(i)xxhat(k))+ha...

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  19. If is the angle between any two vectors -> a and -> b , then ...

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