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Area of a rectangle having vertices : A(...

Area of a rectangle having vertices : `A(-hati+1/2 hatj+4hatk),B(hati+1/2hatj+4hatk),C(hati-1/2 hatj+4hatk),D(-hati-1/2hatj+4hatk)` is :

A

`1/2` square unit

B

1 square unit

C

2 square units

D

4 square units.

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Area of a rectangle having vertices A, B, C and D with position vectors : -hati + (1/2)hatj + 4hatk, hati + (1/2)hatj + 4hatk, hati - (1/2)hatj + 4hatk and -hati - (1/2)hatj + 4hatk , respectively is:

Show that the following vectors are coplanar : -2hati-2hatj+4hatk,-2hati+4hatj-2hatk,4hati-2hatk and hati-hatj+hatk .

Determine whether or not the following pairs of lines intersect : vecr=(hati-2hatj+3hatk)+lambda(-hati+hatj-2hatk) and vecr=(hati-hatj-hatk)+mu(hati+2hatj-2hatk)

If a=3hati-2hatj+hatk,b=2hati-4hatj-3hatk and c=-hati+2hatj+2hatk , then a+b+c is

Consider the equation of the straight lines given by : L_1:vecr=(hati+2hatj+hatk)+lambda(hati-hatj+hatk) L_2:vecr=(2hati-hatj-hatk)+mu(2hati+hatj+2hatk) If veca_1=hati+2hatj+hatk, vecb_1=hati-hatj+hatk, veca_2=2hati-hatj-hatk, vecb_2=2hati+hatj+2hatk , then find : (vecb_1xxvecb_2)*(veca_2-veca_1)

Consider the equation of the straight lines given by : L_1:vecr=(hati+2hatj+hatk)+lambda(hati-hatj+hatk) L_2:vecr=(2hati-hatj-hatk)+mu(2hati+hatj+2hatk) If veca_1=hati+2hatj+hatk, vecb_1=hati-hatj+hatk, veca_2=2hati-hatj-hatk, vecb_2=2hati+hatj+2hatk , then find : veca_2-veca_1

Consider the equation of the straight lines given by : L_1:vecr=(hati+2hatj+hatk)+lambda(hati-hatj+hatk) L_2:vecr=(2hati-hatj-hatk)+mu(2hati+hatj+2hatk) If veca_1=hati+2hatj+hatk, vecb_1=hati-hatj+hatk, veca_2=2hati-hatj-hatk, vecb_2=2hati+hatj+2hatk , then find : vecb_2-vecb_1

Consider the equation of the straight lines given by : L_1:vecr=(hati+2hatj+hatk)+lambda(hati-hatj+hatk) L_2:vecr=(2hati-hatj-hatk)+mu(2hati+hatj+2hatk) If veca_1=hati+2hatj+hatk, vecb_1=hati-hatj+hatk, veca_2=2hati-hatj-hatk, vecb_2=2hati+hatj+2hatk , then find : vecb_1xxvecb_2

MODERN PUBLICATION-VECTORS-Exercise
  1. Let lambda be any non-zero scalar. Then for what possible values of x,...

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  2. Let the vectors veca and vecb be such that |veca|=3 and |vecb|=(sqrt2)...

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  3. Area of a rectangle having vertices : A(-hati+1/2 hatj+4hatk),B(hati+1...

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  4. If theta is the angle between two vectors veca and vecb, then veca c...

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  5. Let veca and vecb be two unit vectors and theta is the angle between t...

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  6. If (hati,hatj,hatk) are the usual three perpendicular unit vectors, th...

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  7. If theta is the angle between two vectors veca and vecb, then |veca*ve...

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  8. The area of the triangle whose adjacent sides are : veca=3hati+hatj+4h...

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  9. The magnitude of the vector 6hati+2hatj+3hatk is :

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  10. The vector with initial point P(2,-3,5) and terminal point Q(3,-4,7) i...

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  11. The angle between the vectors hati-hatj and hatj-hatk is :

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  12. The value of 'lambda' for which the two vectors : 2hati-hatj+2hatk and...

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  13. If |veca|=8,|vecb|=3 and |vecaxxvecb|=12, then value of veca*vecb is :

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  14. If veca=2hati-hatj+hatk and vecb=-2hati+hatk, then the vector in the d...

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  15. If veca and vecb are two collinear vectors, then which of the followi...

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  16. If vecaxxvecb=|veca||vecb|sin theta hatn, which one is correct ?

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  17. If veca*vecb=-|veca||vecb|, then theta=

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  18. The projection of the vector veca=2hati+3hatj+2hatk on the vector vecb...

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  19. The area of triangle having adjacent sides veca and vecb is :

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  20. The magnitude of : veca=3hati+2hatj is :

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