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The position vectors of the points A, B,...

The position vectors of the points A, B, C are `(hati-3hatj-5hatk),(2hati-hatj+hatk)` and `(3hati-4hatj-4hatk)` respectively. Then A, B, C form a/an -

A

equilateral triangle

B

isosceles triangle

C

right angled triangle

D

right angled isosceles triangle

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The correct Answer is:
C
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The position vectors of the points A, B, C and D are hati+3hatj-hatk, -hati-hatj+hatk, 2hati-3hatj+3hatk and -3hati+2hatj+hatk respectively. Then, the ratio of the moduli of the vectors vec(AB) and vec(CD) is -

If the position vectors of the points A, B, C, D are hati+hatj+hatk, 2hati+5hatj, 3hati +2hatj-3hatk and hati-6hatj-hatk respectively, then the angle between the vectors vec(AB) and vec(CD) is -

The position vectors of the vertices A,B,C of the triangle ABC are (hati+hatj+hatk),(hati+5hatj-hatk) and (2hati+3hatj+5hatk) respectively. Find the greatest angle of the triangle.

The position vectors of points A,B and C are hati+hatj+hatk,hati + 5hatj -hatk and 2hati + 3hatj + 5hatk , respectively the greatest angle of triangle ABC is

Show that the points A(-2hati+3hatj+5hatk),B(hati+2hatj+3hatk)andC(7hati-hatk) are collinear.

The position vectors of the three vertices of a triangle are (-hati-3hatj+2hatk), (5hati+7hatj-5hatk) and (2hati+5hatj+6hatk) , then the position vector of the point of intersection of the medians of the triangle is -

The position vectors of the points A,B,C and D are 6 hati - 7 hatj , 16 hati - 29 hatj - 4 hatk , 3 hati - 6 hatk and 2 hati + 5 hatj + 10 hatk respectively. Show that the points A,B,C and D are non coplanar.

If the position vectors of two given points A and B be 4hati+hatj+2hatk and 2hati-5hatj-hatk respectively, then a unit vector in the direction of vec(AB) is -

Show that the points A,B and C with position vectors , veca=3hati-4hatj-4hatk,vecb=2hati-hatj+hatkandvecc=hati-3hatj=5hatk ,respectively form the vertices of a right angled triangle.

Find the sum of the vectors veca=hati-2hatj+hatk,vecb=-2hati+4hatj+5hatkandvecc=hati-6hatj-7hatk .

CHHAYA PUBLICATION-MCQ ZONE -Question Paper 7
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