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(i) If vec(a)=hat(i)+2hat(j)-3hat(k) and...

(i) If `vec(a)=hat(i)+2hat(j)-3hat(k)` and `vec(b)=3hat(i)-hat(j)+2hat(k)`, show that `(vec(a)+vec(b))` is perpendicular to `(vec(a)-vec(b))`.
(ii) If `vec(a)=(5hat(i)-hat(j)-3 hat(k))` and `vec(b)=(hat(i)+3hat(j)-5hat(k))` then show that `(vec(a)+vec(b))` and `(vec(a)-vec(b))` are orthogonal.

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RS AGGARWAL-SCALAR, OR DOT, PRODUCT OF VECTORS-Exercise 23
  1. Find vec(a).vec(b) when (i) vec(a)=hat(i)-2hat(j)+hat(k) and vec(b)=...

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  2. Find the value of lambda for which vec(a) and vec(b) are perpendicular...

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  3. (i) If vec(a)=hat(i)+2hat(j)-3hat(k) and vec(b)=3hat(i)-hat(j)+2hat(k)...

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  4. If vec a= hat a= hat i-\ hat j+7 hat k and vec b=5 hat j-\ hat j+l...

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  5. Show that the vectors vec a=1/7(2 hat i+3 hat j+6 hat k), vec b=1/7(3...

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  6. Let vec(A)=4hat(i)+5hat(j)-hat(k), vec(b)=hat(i)-4hat(j)+5hat(k) and v...

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  7. Let vec(a)=(2hat(i)+3hat(j)+2 hat(k)) and vec(b)=(hat(i)+2hat(j)+hat(k...

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  8. Find the projection of (8hat(i)+hat(j)) in the direction of (hat(i)+2h...

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  9. Write the projection of vector hat i+ hat j+ hat k along the vector ...

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  10. (i) Find the projection of vec(a) on vec(b) if vec(a).vec(b)=8 and vec...

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  11. Find the angle between the vectors vec(a) and vec(b), when (i) vec(a...

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  12. If vec(a)=(hat(i)+2hat(j)-3hat(k)) and vec(b)=(3hat(i)-hat(j)+2hat(k))...

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  13. if veca is a unit vector and (vecx-veca).(vecx+veca)=8 then |vecx|

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  14. Find the angles which the vector vec(a)=3 hat(i)-6hat(j)+2hat(k) makes...

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  15. Show that the vector hat i+ hat j+ hat k is equally inclined with the...

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  16. Find a vector vec a of magnitude 5sqrt(2) making an angle pi/4 with x-...

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  17. Find the angle between (vec(a)+vec(b)) and (vec(a)-vec(b)), if vec(a)=...

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  18. Express the vector vec(a)=(6hat(i)-3hat(j)-6hat(k)) as sum of two vect...

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

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  20. If vec a+ vec b+ vec c=0,| vec a|=3,| vec b|=5,| vec c|=7, then find ...

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