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Question

The points with position vectors 20^i+p^j,5^i^j and 10^i13^j are collinear. The value of p is

A
7
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B
37
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C
7
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D
37
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Solution

The correct option is B 37
20^i+p^j,5^i^j and 10^i13^j are collinear.
[abc]=0 property
a.(b×c)=0
(20^i+p^j).((5^i^j)×(10^i13^j))=0
(20^i+p^j).(65^k+10^k)=0
We can't get up from this
Now,
By using slope method
1p520=13(1)105
1p153=125
p+13=12
p=361=37

1119363_1165790_ans_d193c77c46b84281b21ca140eb0c0456.jpeg

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