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Show that the angle between two diagonal...

Show that the angle between two diagonals of a cube is `cos^(-1)(1/3)dot`

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(i) Find the angle bewteen the lines whose direction ratios are 1, 2, 3 and - 3 , 2 , 1 (ii) Find the angle between two diagonals of a cube.

If veca=(3,1) and vecb=(1,2) represent the sides of a parallelogram then the angle theta between the diagonals of the paralelogram is given by (A) theta=cos^-1(1/sqrt(5)) (B) theta=cos^-1(2/sqrt(5)) (C) theta=cos^-1 (1/(2sqrt(5))) (D) theta = pi/2

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RD SHARMA ENGLISH-SCALAR OR DOT PRODUCT-All Questions
  1. Using dot product of vectors, prove that a parallelogram, whose dia...

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  2. For any three vectors vec a , vec b , vec c , prove that | vec a+ v...

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  3. Show that the angle between two diagonals of a cube is cos^(-1)(1/3)do...

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  4. Find ( vec a+3 vec b).(2 vec a- vec b), If vec a= hat i+ hat j+2 hat ...

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  5. Find the angle between two vectors vec a\ a n d\ vec b having the...

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  6. If hat i+ hat j+ hat k ,\ 2 hat i+5 hat j ,\ 3 hat i+2 hat j-3 hat k\...

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  7. Let vec a\ a n d\ vec b be two vectors of the same magnitude such th...

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  8. Find | vec x| if for a unit vector vec a ,\ ( vec x- vec a)dot \ ( ve...

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  9. If vec a=5 hat i- hat j-3 hat k ,\ a n d\ vec b= hat i+3 hat j-5 hat...

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  10. If vec a+ vec b+ vec c= vec0,\ vec|a|=3,\ | vec b|=5\ a n d\ | vec c...

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  11. For any vector vec a\ a n d\ vec b prove that | vec a+ vec b|lt=| ve...

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  12. For any two vectors vec a and vec b prove that ( veca dot vecb)^2le|...

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  13. If vec a ,\ vec b ,\ are two vectors such that | vec a+ vec b|=| ve...

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  14. The scalar product of the vector vec a= hat i+ hat j+ hat k with a un...

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  15. If vec a ,\ vec b ,\ vec c are three vectors such that vec adot ve...

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  16. Show that the vector 2 hat i- hat j+ hat k ,\ hat i-3 hat j-5 hat k ,...

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  17. Show that the points A, B, C with position vectors 2 hat i- hat j+ ...

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  18. If with reference to a right handed system of mutually perpendicula...

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  19. Find the value of x for which the angle between the vectors vec a=2x^...

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  20. If l ,\ m ,\ n are scalars and vec a ,\ vec b ,\ vec c are vectors,...

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