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

Let `A B C` be triangle, the position vectors of whose vertices are respectively ` hat i+2 hat j+4 hat k` , -2` hat i+2 hat j+ hat k ` and ` 2 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.

Find the area of triangle whose vertices have position vectors hat (i) + hat (j) + 2 hat (k) , 2 hat (i) + 2 hat (j) + 3 hat (k) and 3 hat (i) - hat (j) - hat (k)

Let vec a= hat i+2 hat j+ hat k , vec b= hat i- hat j+ hat ka n d vec c= hat i+ hat j- hat kdot Then find [vec a vec b vec c]

Show that the vectors are mutually perpendicular hat (i) + 2 hat (j) + hat (k) ,hat (i) + hat (j) - 3 hat (k) and 7 hat (i) - 4 hat (j) + hat (k)

If vec a= 2 hat i- hat j+ hat k and vec b = - hat i+3 hat j+4 hat k ,then veca.vecb =

Find the median vec(AD) of the triangle ABC where positive vectors of the vertices A, B and C are respectively hat(i) + hat(j), 4hat(i) + 6hat(j), hat(i) - hat(j)

Find the vector of length 3 unit which is perpendicular to hat i+ hat j+ hat k and lies in the plane of hat i+ hat j+ hat k and 2 hat i-3 hat j .

If vec a=3 hat i- hat j-4 hat k , vec b=2 hat i+4 hat j-3 hat k and vec c= hat i+2 hat j- hat k , find |3 vec a-2 hat b+4 hat c|dot

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

CENGAGE PUBLICATION-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 vectors of whose vertices are re...

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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 a and - hat ...

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

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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^2-6 at...

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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. A straight line L cuts the lines A B ,A Ca n dA D of a parallelogram A...

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

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  20. If vec aa n d vec b are two vectors of magnitude 1 inclined at 120^0 ...

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