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Show that the triangle formed by the vec...

Show that the triangle formed by the vectors `3bar(i)+5bar(j)+2bar(k), 2bar(i)-3bar(j)-5bar(k), -5bar(i)-2bar(j)+3bar(k)` is equilateral.

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The correct Answer is:
the given vectors form an equilateral.
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If the triangle formed by the vectors 3 bar(i) + 5 bar(j) + 2 bar(k) , 2 bar(i) - 3 bar(j) - 5 bar(k) and - 5 bar(i) - 2 bar(j) + 3 bar(k) equilateral ?

The vectors 2bar(i)-3bar(j)+bar(k), bar(i)-2bar(j)+3bar(k), 3bar(i)+bar(j)-2bar(k)

Write the position vector of the centroid of the triangle formed by the points whose position vectors are 3bar(i)+2bar(j)-bar(k), 2bar(i)-2bar(j)+5bar(k), bar(i)+3bar(j)-bar(k) .

Find the value of [bar(i)+bar(j)+bar(k),bar(i)-bar(j),bar(i)+2bar(j)-bar(k)] .

Show that the four points with position vectors 3bar(i)+5bar(j), 3bar(j)-5k, 5bar(i)-19bar(j)-3bar(k), 6bar(i)-5bar(j) are non coplanar.

Show that the points -2bar(i)+3bar(j)+6bar(k), 6bar(i)-2bar(j)+3bar(k), 3bar(i)+6bar(j)-2bar(k) form an equilateral triangle.

Find t, for which the vectors 2bar(i) - 3bar(j) + bar(k), bar(i) + 2bar(j) -3bar(k) , bar(j) - tbar(k) are coplanar.

Find the vector area and area of the triangle with vertices bar(i) + bar(j)-bar(k), 2bar(i)- 3bar(j) + bar(k), 3 bar(i) + bar(j)- 2bar(k) .

Find the position vector of the centroid of the tetrahedron formed by the points 2bar(i)-bar(j)-3bar(k), 4bar(i)+bar(j)+3bar(k), 3bar(i)+2bar(j)-bar(k), bar(i)+4bar(j)+2bar(k) .

The points with P.V's bar(i)+2bar(j)+bar(k), 2bar(i)+3bar(j)+4bar(k) and 4bar(i)+5bar(j)+10bar(k) form

SRISIRI PUBLICATION-SOLVED MODEL PAPER-2-SOLVED MODEL PAPER-2(MATHS-1B)
  1. Show that the triangle formed by the vectors 3bar(i)+5bar(j)+2bar(k), ...

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  2. Transform the equation of x+y+1=0 into Normal form

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  3. Evaluate Lt(x to 0)([x]+x)

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  4. Show that the points A(3,-2,4),B(1,1,1),C(-1,4,-2) are collinear.

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  5. Reduce the equation 4x-4y+2z+5=0 of the plane to the intercept form.

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  6. Compute Lt(x to 0)(3^x-1)/(sqrt(1+x)-1).

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  7. Find {:(" Lt"),(xrarroo):}(8|x|+3x)/(3|x|-2x)

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  8. If y=x^(2)e^(x)sinx, then find dy/dx.

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  9. Find the derivative of Sec^-1(1/(2x^2-1))

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  10. The side of a square is increased from 3 cm to 3.01 cm. Find the appro...

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  11. Verify Rolle's theroem for the function x^2-1 on [-1,1].

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  12. A(5,3) and B(3,-2) are 2 fixed points. Find the equation of locus of P...

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  13. Prove that the angle of rotation of the axes to eliminate xy term from...

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  14. Find the image of (1,2) in the straight line 3x+4y-1=0

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  15. Show that f(x)={{:((cosax-cosbx)/(x^(2))," if " xne0),((1)/(2)(b^(2)...

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  16. Find the derivative of cotx from the first principle.

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  17. A particle moving along a straight line has the relation s=t^(3)+2t+3,...

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  18. Find the equations of the tangent and the normal to the curve y=x^(3)+...

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  19. Find the circumcentre of the triangle whose vertices are (1,3) (0,-2) ...

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  20. Find the centroid and the area of the triangle formed by the lines 2y^...

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  21. Write down the equation of the pair of straight lines joining the orig...

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