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Let A B C be a triangle, the position ve...

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

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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

Let ABC be a triangle, the position vectors of whose vertices are 7hat(j)+10hat(k), -hat(i)+6hat(j)+6hat(k) " and " -4hat(i)+9hat(j)+6hat(k) . Then DeltaABC is -

If the area of the triangle the positive vectors of whose vertices are ahat(j), 4hat(j) and hat(i) + hat(j) is 6 square units, find a.

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 projection of 3hat i - hat j + 4hat k on 2 hat i + 3 hat j -6 hat k

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.

If the points having position vectors hati + b hat j + c hat k , 7 hati + 2 hat j + 6 hat k and 5 hati + 2 hat j + 5 hat k are collinear, find the values of b and c.

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)

The position vectors of point A ,B ,a n dC are hat i+ hat j+ hat k , hat i+5 hat j- hat ka n d2 hat i+3 hat j+5 hat k , respectively. Then greatest angel of triangle A B C is 120^0 b. 90^0 c. cos^(-1)(3//4) d. none of these

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]

CENGAGE PUBLICATION-VECTOR ALGEBRA-All Questions
  1. Statement 1 : If three point P, Q and R have position vectors veca, ve...

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  2. In a four-dimensional space where unit vectors along the axes are h...

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  3. Let A B C be a triangle, the position vectors of whose vertices are -1...

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  4. If non-zero vectors vec a and vec b are equally inclined to coplanar ...

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  5. If A(-4,0,3) and B(14 ,2,-5), then which one of the following points l...

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  6. Prove that the sum of three vectors determined by the medians of a ...

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  7. Prove that the resultant of two forces acting at point O and repres...

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  8. Two forces vec A B and vec A D are acting at vertex A of a quadrilat...

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  9. ABC is a triangle and P any point on BC. If vec(PQ) is the sum of vec(...

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  10. If vector vec a+ vec b bisects the angle between vec a and vec b , ...

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  11. ABCDE is a pentagon. Prove that the resultant of force vec A B , vec...

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  12. if vec (AO) + vec (O B) = vec (B O) + vec (O C) ,than prove that B...

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  13. A unit vector of modulus 2 is equally inclined to x- and y-axes at an ...

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  14. Find the equations of the normal to the curve y=x^3+2x+6 which are par...

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  15. Let vec a , vec b and vec c be unit vectors such that vec a+ vec b- ...

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  16. If the resultant of three forces vec F1=p hat i+3 hat j- hat k , ve...

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  17. Let vec a , vec b , vec c , vec d be the position vectors of the four...

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  18. Statement 1:Let A( vec a),B( vec b)a n dC( vec c) be three points such...

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  19. Statement 1: If | vec a+ vec b|=| vec a- vec b|, then vec a and vec b ...

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  20. Statement 1: vec a=3 vec i+p vec j+3 vec k and vec b=2 vec i+3 vec j...

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