Q20 of 45 Page 1

If and then find the value of λ, so that and are perpendicular vectors.

Given,


and


∴


And


As are perpendicular vectors.


∴ their dot product is going to be 0.


⇒ (( = 0


Finding the dot product by general rule, we get –


⇒ (


⇒


⇒ -24 + 49 – λ2 = 0


⇒ λ2 = 25


∴ λ = ±√25 = ±5


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19

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21

Show that the lines


are intersecting. Hence find their point of intersection.


OR


Find the vector equation of the plane through the points (2, 1, – 1) and (– 1, 3, 4) and perpendicular to the plane x – 2y + 4z =10.

 22

The probabilities of two students A and B coming to the school in time are and respectively. Assuming that the events, ‘A coming in time’ and ‘B coming in time’ are independent, find the probability of only one of them coming to the school in time.

Write at least one advantage of coming to school in time.