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The position vectors of Pa n dQ are 5 ha...

The position vectors of `Pa n dQ` are 5` hat i+4 hat j+a hat k` and `- hat i+2 hat j-2 hat k` , respectively. If the distance between them is 7, then find the value of `adot`

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Given points are `P(5hati+4hatj+ahatk) and Q(-hati+2hatj-2hatk)`
Now `" "vec(PQ)= (-hati+2hatj-2hatk)-(5hati+4hatj+ahatk)`
`" "=(-6hati-2hatj-(2+a)hatk)`
Given `|vec(PQ)|=7`
`therefore" "sqrt(36+4+(a+2)^(2))=7`
or `" "(a+2)^(2)=9 `
or `" "a+2=pm3`
or `" "a=-5, 1`.
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CENGAGE-INTRODUCTION TO VECTORS -Exercise 1.1
  1. Find the unit vector in the direction of the vector veca=hati+hatj+2h...

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  2. Find the direction cosines of the vector hati+2hatj+3hatk.

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  3. Find the direction cosines of the vector joining the points A(1, 2,3) ...

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  4. The position vectors of Pa n dQ are 5 hat i+4 hat j+a hat k and - hat ...

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  5. Given three points are A(-3,-2,0),B(3,-3,1)a n dC(5,0,2)dot Then find ...

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

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

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  8. If A B C D is a rhombus whose diagonals cut at the origin O , then ...

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  9. Let D ,Ea n dF be the middle points of the sides B C ,C Aa n dA B , re...

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  10. Let A B C D be a p[arallelogram whose diagonals intersect at P and ...

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  11. If A B C D is quadrilateral and Ea n dF are the mid-points of A Ca n d...

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  12. If vec A O+ vec O B= vec B O+ vec O C , then A ,Bn a dC are (where O ...

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  13. If the sides of an angle are given by vectors veca=hati-2hatj+2hatk an...

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  14. A B C D is a parallelogram. If La n dM are the mid-points of B Ca n dD...

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  15. A B C D is a quadrilateral. E is the point of intersection of th...

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  16. What is the unit vector parallel to vec a=3 hat i+4 hat j-2 hat k ...

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  17. The position vectors of points Aa n dB w.r.t. the origin are vec a...

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  18. If vec r1, vec r2, vec r3 are the position vectors off thee collinear...

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  19. If veca and vecb are two vectors of magnitude 1 inclined at 120^(@), t...

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  20. Find the vector of magnitude 3, bisecting the angle between the vector...

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