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The scalar product of the vectorhat i+ha...

The scalar product of the vector`hat i+hat j+ hatk` with a unit vector along the sum of vectors `2hat i+4 hat j-5 hatk` and `λ hat i+2 hat j+3 hatk` is equal to one. Find the value of `λ`.

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PRADEEP PUBLICATION-VECTORS-EXERCISE
  1. Show that the direction cosines of a vector equally inclined to the ax...

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  2. Let a=hat(i)+4hat(j)+2hat(k), b=3hat(i)-2hat(j)+7hat(k) and c=2hat(i)-...

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  3. The scalar product of the vectorhat i+hat j+ hatk with a unit vector a...

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  4. If vec a, vec b ,vec c are mutually perpendicular vectors of equal ma...

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  5. Prove that (vec a+vec b)* (vec a+ vec b)=|vec a|^2 +|vec b|^2, if and ...

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  6. If θ is the angle between two vectors vec a and vec b, then vec a*vec ...

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  7. Let vec a and vec b be two unit vectors and θ is the angle between the...

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  8. If (hat i, hat j, hat k) are the usual three perpendicular unit vector...

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  9. If theta is the angle between any two vectors vec(a) and vec(b), "then...

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  10. If vec a is a non-zero vector, then (1/|vec a|) vec a is a..........

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  11. If vec a, vecb are non-collinear vectors, then vec a, vecb and vec a +...

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  12. The vector veca+vecb bisects the angle between the non collinear vecto...

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  13. If vec r* vec a =0 = vec r* vec b ,where vec a and vec b are non-copla...

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  14. If vec r* vec a =0 = vec r* vec b =0 and also vec r* vec c =0 for som...

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  15. If vec a and vec b are any two vectors, then (vec a xx vec b)^2 +(vec ...

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  16. If vec a is any non-zero vector, then (vec a*hat i)hat i + (vec a*hat ...

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  17. If a is any vector, then (a xxhati)^(2)+(axx hatj)^(2)+(axxhatk)^(2)...

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  18. If (atimesb)^(2)+(a*b)^(2)=144 and |a|=4, then find the value of |b|.

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  19. If a non-zero vector vec a makes an angle α with positive direction o...

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  20. The values of k, for which |k vec a| lt |vec a| and k vec a =1/2 vec a...

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