Let a -6 i -3 j -6 k and d - i - j - k-Suppose that a - b - c where b is parallel to d and c is perpendicular to d- Then c isA- 5 i-4 j-k-B- 7 i-2 j-5 k-C- 4 i-5 j-k-D- 3 i-6 j-9 k-

The correct option is B a⃗=6i⃗ 3j⃗ 6k⃗ d⃗=i⃗+j⃗+k⃗ a⃗=b⃗+c⃗...............(1) b⃗=λd⃗ & c⃗.d⃗=0 b⃗=λî+λĵ+λk̂ From (1) 6î 3ĵ 6k̂=λî+λĵ+λk̂+c⃗ c⃗=(6 λ)î ...

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Byju's Answer

Standard XII

Mathematics

Applications of Dot Product

Let a =6 i -3...

Question

Let $\to a = 6 \to i - 3 \to j - 6 \to k$ and $\to d = \to i + \to j + \to k$ .Suppose that $\to a = \to b + \to c$ where $\to b$ is parallel to $\to d$ and $\to c$ is perpendicular to $\to d$ . Then $\to c$ is

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Solution

The correct option is B
$\to a = 6 \to i - 3 \to j - 6 \to k \to d = \to i + \to j + \to k \to a = \to b + \to c . . . . . . . . . . . . . . . (1) \to b = λ \to d & \to c . \to d = 0 \to b = λ^i + λ^j + λ^k F r o m (1) 6^i - 3^j - 6^k = λ^i + λ^j + λ^k + \to c \to c = (6 - λ)^i - (3 + λ)^j - (6 + λ)^k \to c . \to d = 0 \Rightarrow λ = - 1 \to c = 7^i - 2^j - 5^k$

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Similar questions

Q. Decompose the vector

\to b = 6 ˆ i - 3 ˆ j - 6 ˆ k

into two vectors,

\to c

and

\to d

, one of which is parallel and the other perpendicular to the vector

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Q. Let

\to a = 6 \to i - 3 \to j - 6 \to k

and

\to d = \to i + \to j + \to k .

Suppose that

\to a = \to b + \to c

where

\to b is parallel to \to d and \to c is perpendicular to \to d .

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\to c

Q. Show that the points whose position vectors

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Q. Let

\to a = 6 \to i - 3 \to j - 6 \to k

and

\to d = \to i + \to j + \to k

. Suppose that

\to a = \to b + \to c

where

\to b

is parallel to

\to d

and

\to c

is perpendicular to

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\to c

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form:

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Let →a=6→i−3→j−6→k and →d=→i+→j+→k.Suppose that →a=→b+→c where →b is parallel to →d and →c is perpendicular to →d. Then →c is

The correct option is B →a=6→i−3→j−6→k→d=→i+→j+→k→a=→b+→c...............(1)→b=λ→d & →c.→d=0→b=λ^i+λ^j+λ^kFrom(1)6^i−3^j−6^k=λ^i+λ^j+λ^k+→c→c=(6−λ)^i−(3+λ)^j−(6+λ)^k→c.→d=0⇒λ=−1→c=7^i−2^j−5^k

Let $\to a = 6 \to i - 3 \to j - 6 \to k$ and $\to d = \to i + \to j + \to k$ .Suppose that $\to a = \to b + \to c$ where $\to b$ is parallel to $\to d$ and $\to c$ is perpendicular to $\to d$ . Then $\to c$ is