If b- is the vector whose initial point divides the joining 5- and 5- in the ratio - - 1 and terminal point is at origin- lf -b-37- then -

If $\to b$ is a vector whose initial point divides the join of $5^i$ and $5^j$ in the ratio $k : 1$ and whose terminal point is the origin and $| \to b | \leq \sqrt{37}$ , then $k$ lies in the interval

Q. If

\to b

is a vector whose initial point divides the join of

5^i

and

5^j

in the ratio

k : 1

and whose terminal point is the origin and

| \to b | \leq \sqrt{37}

, then

k

lies in the interval

Q. If

\to b

is the vector whose initial point divides the joining

5 \to i

and

5 \to j

in the ratio

λ : 1

and terminal point is at origin. If

| \to b | \leq \sqrt{37},

then set of values of

λ

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If →b is the vector whose initial point divides the joining 5^i and 5^j in the ratio λ: 1 and terminal point is at origin. lf |→b|≤√37, then λ∈.

The correct option is A (−∞,−6]∪[−16,∞)Apply section formula and we get,→b=5^i+5λ^jλ+1|→b|≤√37∴ 25×λ2+25≤(λ+12)×37 ∴ 25×λ2+25≤37×(λ2+2λ+1)∴ 25×λ2+25≤37×λ2+74λ+37∴12×λ2+74λ+12≥0.∴6×λ2+37λ+6≥0 ∴λ∈(−∞,−6]∪[−16,∞)

If $\to b$ is the vector whose initial point divides the joining $5^i$ and $5^j$ in the ratio $λ :$ $1$ and terminal point is at origin. lf $| \to b | \leq \sqrt{37}$ , then $λ \in$ .