Let ABCD be a parallelogram such that A-B-q-A-D-p- and - BAD be an acute angle- If r- is the vector that coincides with the altitude directed from the vertex B to the side AD- then r- is given by

The correct option is D r⃗= q⃗+(p⃗.q⃗)(p⃗.p⃗)p⃗ Let 'E' be the point between A and D such that BE⊥ AD #160;A⃗E⃗= vector compo ...

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Byju's Answer

Standard XII

Mathematics

Addition of Vectors

Let ABCD be...

Question

Let $A B C D$ be a parallelogram such that $\to A B = \to q, \to A D = \to p$ and $∠ B A D$ be an acute angle. If $\to r$ is the vector that coincides with the altitude directed from the vertex $B$ to the side $A D$ , then $\to r$ is given by

\to r = 3 \to q - \frac{3 (\to p . \to q)}{(\to p . \to p)} \to p

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\to r = - \to q + \frac{(\to p . \to q)}{(\to p . \to p)} \to p

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\to r = \to q - \frac{(\to p . \to q)}{(\to p . \to p)} \to p

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\to r = - 3 \to q + \frac{3 (\to p . \to q)}{(\to p . \to p)} \to p

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Solution

The correct option is D $\to r = - \to q + \frac{(\to p . \to q)}{(\to p . \to p)} \to p$
Let $^{'} E^{'}$ be the point between $A$ and $D$ such that $B E ⊥ A D$
$\to A E =$ vector component of $\to q$ on $\to p$
$\to A E = (\frac{\to p \cdot \to q}{\to p \cdot \to p}) \to p$
In $Δ A B E, \to A B + \to B E = \to A E$
$\to q + \to r = (\frac{\to p \cdot \to q}{\to p \cdot \to p}) \to p$
$\to r = - \to q + (\frac{\to p \cdot \to q}{\to p \cdot \to p}) \to p$
Hence, option $^{'} B^{'}$ is correct.

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Similar questions

Q. Let ABCD be a parallelogram such that

\to A B = q, \to A D = \to p

and

∠

BAD be an acute angle. If

\to r

is the vector that coincide with the altitude directed from the vertex B to the side AD, then

\to r

is given by?

Q. Given that

P = Q = R

. If

\to P + \to Q = \to R

then the angle between

\to P

and

\to R

θ_{1}

. If

\to P + \to Q + \to R = \to 0

then the angle between

\to P

and

\to R

θ_{2}

. The relation between

θ_{1}

and

θ_{2}

Q. If

[\to p + 2 \to q + 3 \to r \to q + 2 \to r + 3 \to p \to r + 2 \to p + 3 \to q] = 54

where

\to p

\to q

and

\to r

are three vector then the Value of

∣ ∣ ∣ ∣ \begin{matrix} \to p . \to p & \to p . \to q & \to p . \to r \to p . \to q & \to q . \to q & \to q . \to r \to p . \to r & \to r . \to q & \to r . \to r \end{matrix} ∣ ∣ ∣ ∣

Q. Three vectors

\to P

\to Q

\to R

are such that the

| \to P |

= | \to Q |

| \to R |

= \sqrt{2}

| \to P |

and

\to P + \to Q

+ \to R = 0

. The angle between

\to P

and

\to Q

\to Q

and

\to R

and

\to P

and

\to R

will be respectively.

Q. Let

\to p, \to q, \to r

be three mutually perpendicular vectors of the same magnitude. If a vector

\to x

satisfies the equation

\to p [(\to x - \to q) \times \to p] + \to q \times [(\to x - \to r) \times \to q] + \to r \times [(\to x - \to p) \times \to r] = \to 0

, then

\to x

is given by

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Let ABCD be a parallelogram such that →AB=→q,→AD=→p and ∠BAD be an acute angle. If →r is the vector that coincides with the altitude directed from the vertex B to the side AD, then →r is given by

Let $A B C D$ be a parallelogram such that $\to A B = \to q, \to A D = \to p$ and $∠ B A D$ be an acute angle. If $\to r$ is the vector that coincides with the altitude directed from the vertex $B$ to the side $A D$ , then $\to r$ is given by