Q6 of 25 Page 10

If and , then show that the vectors and are perpendicular.

Given: and


To prove: and are perpendicular


Formula used:


If two vectors are perpendicular, their dot product is zero


Hence,



Therefore,










= 24 – 8 – 16


= 24 – 24


= 0


Since,



are perpendicular to each other


Hence Proved


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Write the projection of vector on the vector .

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Write the value of .

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If θ is the angle between the vectors and , then find the value of tan θ.

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Consider two points P and Q with position vectors and . Find the position vector of a point R which divides the line segment joining P and Q in the ratio 2:1,

(i) Internally


(ii) Externally


(i) Internally