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If the position vectors of the points A, B C are `3hat(i)-4hat(j)-4hat(k), 2hat(i)-hat(j)+hat(k) " and " hat(i)-3hat(j)-5hat(k)` respectively. Show that ABC is right-angled triangle.

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If the position vectors of the points A, B, C are -2hat(i)+2hat(j)+2hat(k), 2hat(i)+3hat(j)+3hat(k) " and " -hat(i)-2hat(j)+3hat(k) respectively, show that ABC is an isosceles triangle.

The position vectors of the points A,B, and C are 2hat(i)+4hat(j)-hat(k), 4hat(i)+5hat(j)+hat(k) " and " 3hat(i)+6hat(j)-3hat(k) respectively. Show that the points form a right-angled triangle.

The position vectors of the points A, B and C are 2hat(i)+6hat(j)-hat(k), hat(i)+2hat(j)+4hat(k) " and " 3hat(i)+10hat(j)-6hat(k) respectively. Show that the points A, B and C are collinear.

(i) If the position vectors of the points A, B, C be 5hat(i)+3hat(j)+4hat(k), hat(i)+5hat(j)+hat(k) " and " -3hat(i)+7hat(j)-2hat(k) respectively, then show that the points B bisects the line-segment bar(AC) . (ii) The position vectors of the points P and Q are 5hat(i)-12hat(j)+5hat(k) " and " -4hat(i)+3hat(j)-hat(k) respectively. Find the position vectors of the trisection points of the line-segment bar(PQ) .

The position vectors of the points A, B, C and D are hat(i)+hat(j)+hat(k), 2hat(i)+3hat(j), 3hat(i)+5hat(j)-2hat(k) " and " -hat(j)+hat(k) respectively. Show that vec(AB) " and " vec(CD) are parallel and find the ratio of their moduli.

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

If the position vectors of the points P and Q are 2hat(i)+hat(k) " and " -3hat(i)-4hat(j)-5hat(k) respectively, then vector vec(OP) is -

The position vectors of the points A, B and C are -5hat(i)+hat(j), 5hat(i)+5hat(j) " and " 10hat(i)+7hat(j) , show that the points A, B, C are colinear.

The position vectors of the points A and B are 3hat(i)-hat(j)+7hat(k) " and " 4hat(i)-3hat(j)-hat(k) , find the magnitude and direction cosines of vec(AB)

Show that the poins whose position vectors are 4hat(i)+5hat(k),hat(i)+hat(j)+3hat(k)" and "-5hat(i)+3hat(j)-hat(k) are collinear.

CHHAYA PUBLICATION-VECTOR-EXERCISE - SHORT ANSWER TYPE QUESTIONS
  1. If vec(a)=hat(i)+2hat(j)-hat(k) " and " vec(b)=3hat(i)+hat(j)-5hat(k),...

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  2. Let vec(a)=4hat(i)+3hat(j)-hat(k), vec(b)=5hat(i)+2hat(j)+2hat(k), vec...

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

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  4. If the position vectors of the points A, B C are 3hat(i)-4hat(j)-4hat(...

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  5. If vec(a), vec(b), vec(c) are three given vectors, show that the point...

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  6. If vec(a)=hat(i)+hat(j)-4hat(k) " and " vec(b)=4hat(i)-hat(j)-2hat(k),...

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  7. If the position vectors of the points A, B, C are -2hat(i)+2hat(j)+2ha...

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  8. If the coordinates of the points A, B and C are (2, 6, 3), (1, 2, 7) ...

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  9. The position vectors of three points are (a) -2hat(i)+3hat(j)+5hat(k...

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  10. If the vectors phat(i)-5hat(j)+6hat(k) " and " 2hat(i)-3hat(j)-qhat(k)...

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  11. If the points having position vectors hat(i)+bhat(j)+chat(k), 7hat(i)+...

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  12. The position vecors of the points A and B are 4hat(i)-3hat(j)+5hat(k) ...

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  13. If vec(AB)=2hat(i)-4hat(j)+5hat(k) " and " vec(BC)=hat(i)-2hat(j)-3hat...

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  14. The position vectors of the points A and B are 2vec(a)+vec(b) " and " ...

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  15. Show that the vector hat(i)+hat(j)+hat(k) makes the same angle with th...

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  16. Let D, E, F are the midpoints of the sides bar(BC), bar(CA) " and " ba...

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  17. If vec(AO)+vec(OB)=vec(BO)+vec(OC), show that the points A, B and C ar...

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