Given A- - 2- - p- - qk- and B-5-7- - 3k- If A- B- then the values of p and q are- respectively-

The correct option is A 145 and 65 Given #160; A⃗ =2↑ +pĵ +qk̂ B⃗ =5↑ +7ĵ +3k̂ A∥ B⇒ A× B=0 Take AB and simplifying, ∴ #1 ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Physics

Multiplication with Vectors

Given A⃗ = ...

Question

Given $\to A = 2^i + p^j + q^k$ and $\to B = 5^i + 7^j + 3^k$ . If $\to A | | \to B$ , then the values of $p$ and $q$ are, respectively,

\frac{14}{5}

and

\frac{6}{5}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

\frac{14}{3}

and

\frac{6}{5}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{6}{5}

and

\frac{1}{3}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{3}{4}

and

\frac{1}{4}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A $\frac{14}{5}$ and $\frac{6}{5}$
Given $\to A = 2 ↑ + p^j + q^k \to B = 5 ↑ + 7^j + 3^k$
$A ∥ B \Rightarrow A \times B = 0$

Take $det A B$ and simplifying,

$∴$ $3 p - 7 q = 0$ and $6 - 5 q = 0$ and $14 - 5 p = 0$
$\Rightarrow q = \frac{6}{5}$ $p = \frac{14}{5}$

Suggest Corrections

Similar questions

Q. If

\to a

and

\to b

are vectors in space given by

\to a = \frac{^i - 2^j}{\sqrt{5}}

and

\to b = \frac{2^i +^j + 3^k}{\sqrt{14}}

, then the value of

(2 \to a + \to b) . [(\to a \times \to b) \times (\to a - 2 \to b)]

Q. If

\to a

and

\to b

are vector is space given by

\to a = \frac{^i - 2^j}{\sqrt{5}}

and

\to b = \frac{2^i +^j + 3^k}{\sqrt{14}},

then the value of

(2 \to a + \to b) . [(\to a \times \to b) \times (\to a - 2 \to b)]

\to a = 2^i +^j + 3^k, \to b = p^i +^j + q^k

and

\to b \times \to a = \to 0

, then

Q. If

\to A = 5^i + 7^j - 3^k

and

\to B = 2^i + 2^j + a^k

are perpendicular vectors then the value of

a

is:

Q. Magnitudes of vectors

\to a, \to b, \to c

are

3, 4, 5

respectively. If

\to a

and

\to b + \to c

\to b

and

\to c + \to a

\to c

and

\to a + \to b

are mutually perpendicular, then the magnitude of

\to a + \to b + \to c

is,

Join BYJU'S Learning Program

Given →A=2^i+p^j+q^k and →B=5^i+7^j+3^k. If →A||→B, then the values of p and q are, respectively,

The correct option is A 145 and 65Given →A=2↑+p^j+q^k→B=5↑+7^j+3^kA∥B⇒A×B=0Take detAB and simplifying,∴ 3p−7q=0 and 6−5q=0 and 14−5p=0 ⇒q=65 p=145

Given $\to A = 2^i + p^j + q^k$ and $\to B = 5^i + 7^j + 3^k$ . If $\to A | | \to B$ , then the values of $p$ and $q$ are, respectively,

The correct option is A $\frac{14}{5}$ and $\frac{6}{5}$
Given $\to A = 2 ↑ + p^j + q^k \to B = 5 ↑ + 7^j + 3^k$
$A ∥ B \Rightarrow A \times B = 0$

Take $det A B$ and simplifying,

$∴$ $3 p - 7 q = 0$ and $6 - 5 q = 0$ and $14 - 5 p = 0$
$\Rightarrow q = \frac{6}{5}$ $p = \frac{14}{5}$