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Show that the vectors 2hat(i) + 3hat(j),...

Show that the vectors `2hat(i) + 3hat(j), 5hat(i) - 5hat(k)` and `6hat(j) + 4hat(k)` are coplanar.

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The correct Answer is:
Hence, given vectors are coplannar.
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Show that the vectors -hat(i) + hat(j) - hat(k), hat(i) + hat(j) + hat(k) and hat(i) + hat(k) are coplanar.

Show that the vectors 2hat(i)-3hat(j)+4hat(k) and -4hat(i)+6hat(j)-8hat(k) are collinear.

Prove that the four points with position vectors hat(i) + hat(j) + 3hat(k) , hat(i) - 2hat(j) + 2hat(k) and 2hat(i) + 2hat(k) are coplanar.

Show that the vectors vec(a) = hat(i) - 2hat(j) + 3hat(k), vec(b) = -2hat(i) + 3hat(j) - 4hat(k) and vec(c) = hat(i) - 3hat(j) + 5hat(k) are coplanar.

Show that the vectors vec(a) = 3hat(i) - 2hat(j) + hat(k), vec(b) = hat(i) - 3hat(j) + 5hat(k) and vec(c) = 2hat(i) + hat(j) - 4hat(k) form a right angled triangle.

Prove that the vectors 2hat(i) - hat(j) + hat(k), hat(i) - 3hat(j) - 5hat(k), 3hat(i) - 4hat(j) - 4hat(k) are the sides of a right angled triangle.

ARIHANT PRAKASHAN-VECTORS -TOPIC -2 (PRACTICE QUESTIONS) (1 MARK QUESTIONS)
  1. Find the scalar projection of the vector vec a= 3 hat i+6 hat j+9 hat ...

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  2. Determine mu, for which the vector vec(a)=mu(6hat(i)+2hat(j)-3hat(k)) ...

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  3. Show that the vectors 2hat(i) + 3hat(j), 5hat(i) - 5hat(k) and 6hat(j)...

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  4. If vec(a).vec(b) = 0 and vec(a) xx vec(b) = vec(0), then draw the conc...

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  5. If vec(a)xxvec(b)=vec(b)xxvec(c )!=vec(0), then prove that vec(a)+ve...

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  6. What is the angle between the vectors 2hat(i) - hat(j) - hat(k) and ha...

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  7. Determine the area of the parallelogram whose sides are the vectors 2h...

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  8. Using vector method find the area of the triangle with vertices (1, 0,...

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  9. Write the angle between vec(a) and vec(c ), if vec(a)xx(vec(b)xxvec(c ...

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  10. What is (hat(i)-hat(j))*(hat(j)-hat(i)) ?

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  11. (2hat(i)-4hat(j))*(hat(i)+hat(j)+hat(k))= . . . .

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  12. If vec(a)=hat(i)+2hat(j)-hat(k),vec(b)=hat(i)+hat(j)+2hat(k),vec(c )=2...

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  13. Each question given below have four possible answers, out of which onl...

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  14. Each question given below have four possible answers, out of which onl...

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  15. Each question given below have four possible answers, out of which onl...

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  16. (-vec(a))*vec(b)xx(-vec(c))= . . . .

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  17. For the non-zero vectors vec(a),vec(b) and vec(c ),vec(a)*(vec(b)xxvec...

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  18. What is the projection of hat i + hat j - hat k upon the vector hat i ...

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  19. If hat(a) is a unit vector and (vec(x) - hat(a)).(vec(x) + hat(a)) = 8...

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  20. If |vec(a)|=sqrt(3),|vec(b)|=2 and vec(a)*vec(b)=3, then find the angl...

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