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The two adjacent sides of a parallelogra...

The two adjacent sides of a parallelogram are `2 hat i-4 hat j+5 hatk` and `hat i-2hat j-3 hatk`. Find the unit vector Parallel to its diagonal. Also, find its area.

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The sides of a parallelogram represent the vectors 2 hat i- 4 hat j+ 5 hat k and hat i- 2 hat j-3 hat k . Find the unit vectors parallel to its diagonals.

The two adjacent sides of a parallelogram are given by the vectors 2hati-4hatj+5hatk and hati-2hatj-3hatk Find a unit vector parallel to its diagonal (longer). Also find the area of parallelogram.

The area of the parallelogram whose adjacent sides are hat i+hat k and 2hat i+ hatj +hat k ts

If vec a=4 hat i -hat j +hat k and vec b =2hat i-2 hat j+hat k , then find a unit vector vec a+ vec b .

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Find the angle between the vectors 2 hat i -hat j+ hat k and 3 hat i +4hat j - hat k

For given vectors, vec a =2 hat i- hat j+2hat k and vec b =-hat i +hat j - hat k , find the unit vector in the direction of the vector vec a+ vec b .

Find p if the vectors 2 hat i +3 hat j + 6 hat k and p hat i+2 hat j-3 hat k are perpendicular.

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PRADEEP PUBLICATION-VECTORS-EXERCISE
  1. Show that the points A (1, - 2, - 8), B (5, 0,- 2) and C (11, 3, 7) ar...

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  2. Find the position vector of a point R which divides the line joining t...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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