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If the angle between vec(a) and vec(b) i...

If the angle between `vec(a) and vec(b)` is `(pi)/(6) and vec(c)=vec(a)+3vec(b)`, then `c^(2)=`

A

`a^(2)+sqrt(3)ab+ab^(2)`

B

`a^(2)+2sqrt(3)ab+b^(2)`

C

`a^(2)+3ab+b^(2)`

D

`a^(2)+3sqrt(3)ab+9b^(2)`

Text Solution

Verified by Experts

The correct Answer is:
D
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NIKITA PUBLICATION-VECTOR-MULTIPLE CHOICE QUESTIONS
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  2. If the angle between overline(a) and overline(b) is (P1)/(4) and overl...

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  3. If the angle between vec(a) and vec(b) is (pi)/(6) and vec(c)=vec(a)+3...

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  4. If overline(b)=overline(a)-4overline(c) and angle between overline(a) ...

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  5. If the position vectors of the vertices of a triangle be 2hat(i)+4hat(...

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  6. If 7hat(j)+10hat(k), -hat(i)+6hat(j)+6hat(k) and -4hat(i)+9hat(j)+6hat...

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  7. Let alpha,beta,gamma be distinct real numbers. The points with positio...

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  8. The perimeter of the triangle with sides 3hat(i)+4hat(j)+5hat(k), 4hat...

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  9. The perimeter of the triangle whose vertices have the position vectors...

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  10. Let overline(lambda)=overline(a)times(overline(b)+overline(c)), overli...

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  11. |[overline(a)*overline(a), overline(a)*overline(b)], [overline(a)*over...

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  12. The value of |[overline(a)*overline(a), overline(a)*overline(b), overl...

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  13. If overline(a), overline(b), overline(c) be three vecotrs such that ov...

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  14. If |overline(a)|=50 and overline(b)=6hat(i)-8hat(j)-(15)/(2)hat(k) are...

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  15. If overline(a) and overline(b) are the position vectors of the points ...

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  16. If the vectors 3hat(i)-5hat(j)+hat(k)and9hat(i)-15hat(j)+phat(k) are c...

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  17. If the vectors 2hat(i)-qhat(j)+3hat(k)and4hat(i)-5hat(j)+6hat(k) are c...

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  18. The value of k for which the vectors overline(a)=hat(i)-hat(j) and ove...

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  19. Let overline(a) and overline(b) be non-collinear. If overline(c)=(x-2)...

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  20. If the points A(3, 2, -4), B(9, 8, -10) and C(-2, -3. p) are collinear...

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