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Army Group X Practice Set 1

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Question : 70 of 70

Marks: +1, -0

The position vectors of the points

A, B

C

(2\hat{i}+\hat{j}-\hat{k})

(3\hat{i}-2\hat{j}+\hat{k})

(\hat{i}+4\hat{j}-3\hat{k})

form an isosceles triangle
form a right angled triangle
are collinear
form a scalene triangle

Solution:

(c)

AB=(3-2)\hat{i}+(-2-1)\hat{j}+(1+1)\hat{k}

=\hat{i}-3\hat{j}+2\hat{k}

B C\;\; =(1-3)\hat{i}+(4+2)\hat{j}+(-3-1)\hat{k}

\;\; =-2\hat{i}+6\hat{j}-4\hat{k}

C A\;\; =(2-1)\hat{i}+(1-4)\hat{j}+(-1+3)\hat{k}

\;\; =\hat{i}-3\hat{j}+2\hat{k}

|A B|\;\; =\sqrt{1+9+4}=\sqrt{14}

|B C|\;\; =\sqrt{4+36+16}=\sqrt{56}=2\sqrt{14}

|C A|=\sqrt{1+9+4}=\sqrt{14}

\therefore A B+A C=B C

Hence,

A, B

and

C

are collinear.

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