If vec a= 2 hati+3 hatj- hat k, vec b = hat i+2 hat j-5 hat k , vec c =3 hat i+ 5 hat j- hat k, then a vector perpendicular to veca and in the plane containing vec b and vec c is

Question

If vec a= 2 hati+3 hatj- hat k, vec b = hat i+2 hat j-5 hat k , vec c =3 hat i+ 5 hat j- hat k, then a vector perpendicular to veca and in the plane containing vec b and vec c is (A) 17 hat i+21 hatj -123 hat k (B) -17 hat i+21 hatj -97 hat k (C) -17 hat i-21 hatj -97 hat k (D) -17 hat i-21 hatj +97 hat k

Tardigrade Admin · Accepted Answer

We know that a vector perpendicular to a and in the plane containing

b

and

c

is given by

a \times (b \times c) .

Given

a = 2 \hat{i} + 3 \hat{j} - \hat{k}

b = \hat{i} + 2 \hat{j} - 5 \hat{k}

and

c = 3 \hat{i} + 5 \hat{j} - \hat{k}

∴ b \times c = ∣ ∣ \hat{i} 13 \hat{j} 25 \hat{k} - 5 - 1 ∣ ∣ = 23 \hat{i} - 14 \hat{j} - \hat{k}

Now,

a \times (b \times c) = ∣ ∣ \hat{i} 223 \hat{j} 3 - 14 \hat{k} - 1 - 1 ∣ ∣

= (- 3 - 14) \hat{i} - \hat{j} (- 2 + 23) + \hat{k} (- 28 - 69)

= - 17 \hat{i} - 21 \hat{j} - 97 \hat{k}

Which is the required vector.

Q. If $a = 2 \hat{i} + 3 \hat{j} - \hat{k}, b = \hat{i} + 2 \hat{j} - 5 \hat{k}, c = 3 \hat{i} + 5 \hat{j} - \hat{k},$ then a vector perpendicular to $a$ and in the plane containing $b$ and $c$ is

$17 \hat{i} + 21 \hat{j} - 123 \hat{k}$

$- 17 \hat{i} + 21 \hat{j} - 97 \hat{k}$

$- 17 \hat{i} - 21 \hat{j} - 97 \hat{k}$

$- 17 \hat{i} - 21 \hat{j} + 97 \hat{k}$

Q. If a=2i^+3j^​−k^,b=i^+2j^​−5k^,c=3i^+5j^​−k^, then a vector perpendicular to a and in the plane containing b and c is

17i^+21j^​−123k^

−17i^+21j^​−97k^

−17i^−21j^​−97k^

−17i^−21j^​+97k^

Q. If $a = 2 \hat{i} + 3 \hat{j} - \hat{k}, b = \hat{i} + 2 \hat{j} - 5 \hat{k}, c = 3 \hat{i} + 5 \hat{j} - \hat{k},$ then a vector perpendicular to $a$ and in the plane containing $b$ and $c$ is

$17 \hat{i} + 21 \hat{j} - 123 \hat{k}$

$- 17 \hat{i} + 21 \hat{j} - 97 \hat{k}$

$- 17 \hat{i} - 21 \hat{j} - 97 \hat{k}$

$- 17 \hat{i} - 21 \hat{j} + 97 \hat{k}$