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Let A B C be triangle, the position vecr...

Let `A B C` be triangle, the position vecrtors of whose vertices are respectively ` hat i+2 hat j+4 hat k` , -2` hat i+2 hat j+ hat ka n d2 hat i+4 hat j-3 hat k` . Then `"Delta"A B C` is a. isosceles b. equilateral c. right angled d. none of these

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Let A B C be a triangle, the position vectors of whose vertices are -10 hat i+10 hat k ,- hat i+6 hat j+6 hat k and -4 hat i+9 hat j+6 hat k . Then Delta A B C is a. isosceles b. equilateral c. right angled d. none of these

Prove that point hat i +2 hat j - 3 hat k ,2 hat i - hat j + hat k and 2 hat i + 5 hat j - hat k from a triangle in space.

Prove that the following vectors are coplanar: hat i+ hat j+ hat k ,\ 2 hat i+3 hat j- hat k\ a n d- hat i-2 hat j+2 hat k

Find the projection of vec b+ vec c on vec a , where vec a = 2 hat i-2 hat j+ hat k , vec b = hat i+2 hat j-2 hat k and vec c=2 hat i- hat j+4 hat k .

Write the projection of vec b+ vec c\ on\ vec a , when vec a=2 hat i-2 hat j+ hat k ,\ vec b= hat i+2 hat j-2 hat k\ a n d\ vec c=2 hat i- hat j+4 hat kdot

Find the projection of vec b+ vec c on vec a where vec a=2 hat i-\ 2 hat j+\ hat k ,\ vec b=\ hat i+\ 2 hat j-\ 2 hat k and vec c=2 hat i-\ hat j+\ 4 hat k

Check whether the three vectors 2 hat i+2 hat j+3 hat k ,-3 hat i+3 hat j+2 hat ka n d3 hat i+4 hat k from a triangle or not

The position vectors of the points A ,\ B ,\ C are 2 hat i+ hat j- hat k ,\ 3 hat i-2 hat j+ hat k\ a n d\ hat i+4 hat j- hat k respectively. These points a.Form an isosceles triangle b.Form a right triangle c.Are collinear d.Form a scalene triangle

Show that the vectors vec a=-2 hat i-2 hat j+4 hat k ,\ vec b=-2 hat i+4 hat j-2 hat k\ a n d\ vec c=4 hat i-2 hat j-2 hat k are coplanar.

Find vec a.( vec bxx vec c)\ if\ vec a=2 hat i+ hat j+3 hat k ,\ vec b=- hat i+2 hat j+ hat k\ a n d\ vec c=3 hat i+ hat j+2 hat kdot

CENGAGE ENGLISH-VECTOR ALGEBRA-All Questions
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  2. If G is the centroid of triangle A B C ,t h e n vec G A+ vec G B+ vec ...

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  3. Let A B C be triangle, the position vecrtors of whose vertices are ...

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  4. If | vec a+ vec b|<| vec a- vec b|, then the angle between vec aa...

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  5. ' I ' is the incentre of triangle A B C whose corresponding sides are ...

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  6. Let x^2+3y^2=3 be the equation of an ellipse in the x-y plane. Aa n dB...

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  7. Locus of the point P, for which vec(OP) represents a vector with direc...

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  8. If vec xa n d vec y are two non-collinear vectors and A B C isa trian...

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  9. If hat i-3 hat j+5 hat k bisects the angle between hat aa n d- hat ...

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  10. If 4 hat i+7 hat j+8 hat k ,2 hat i+3 hat j+24a n d2 hat i+5 hat j+7 h...

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  11. If vec b is a vector whose initial point divides thejoin of 5 hat i...

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  12. Find the value of lambda so that the points P ,Q ,R and S on the sides...

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  13. A uni-modular tangent vector on the curve x=t^2+2,y=4t-5,z=2t^2-6t=...

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  14. If vec xa n d vec y are two non-collinear vectors and a, b, and c r...

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

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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. ABCD  is a quadrilateral and  E  is the point of intersection of ...

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  18. ABCD is a parallelogram. If L and M be the middle points of BC and CD,...

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  19. If vec a , vec b , vec ca n d vec d are four vectors in three-dimensi...

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

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