COMPASSLearning

Talk to us Register Login

JEE Main · 2019 · 09 Jan 2019 · Shift 1 · Vector Algebra

Let

a = \hat{i} - \hat{j}, b = \hat{i} + \hat{j} + \hat{k}

and

c

be a vector such that

a \times c + b = 0

and

a \cdot c = 4

, then

∣ c ∣^{2}

is equal to:

(A) $\frac{19}{2}$ ✓ Correct
(B)9
(C)8
(D) $\frac{17}{2}$

Answer: (A)

Solution

Let

c = x \hat{i} + y \hat{j} + z \hat{k}

. Computing

a \times c

with

a = \hat{i} - \hat{j}

gives

- z \hat{i} - z \hat{j} + (x + y) \hat{k}

, so

a \times c + b = 0

forces

z = 1

and

x + y = - 1

. The dot condition

a \cdot c = x - y = 4

then gives

x = \frac{3}{2}

and

y = - \frac{5}{2}

. Therefore

∣ c ∣^{2} = \frac{9}{4} + \frac{25}{4} + 1 = \frac{19}{2}

.

JEE Main · 2019 · 09 Jan 2019 · Shift 1 · Single correct option

Practise more: all JEE Main PYQs on Vector Algebra →

More JEE Main questions on Vector Algebra

Let $a = - \hat{i} + 2 \hat{j} + 2 \hat{k}, b = 8 \hat{i} + 7 \hat{j} - 3 \hat{k}$ and $c$ be a vector such that $a \times c = b$ . If …
JEE Main 2026View solution →
Let $c$ and $d$ be vectors such that $∣ c + d ∣ = 29$ and …
JEE Main 2026View solution →
For a triangle $A B C$ , let $p = B C, q = C A$ and $r = BA$ . If $∣ p ∣ = 23, ∣ q ∣ = 2$ and $cos θ = \frac{1}{3}$ , where $θ$ …
JEE Main 2026View solution →
Let $A B = 2 \hat{i} + 4 \hat{j} - 5 \hat{k}$ and $AD = \hat{i} + 2 \hat{j} + λ \hat{k}, λ \in R$ . Let the projection of the vector …
JEE Main 2026View solution →
Let $a = 2 \hat{i} - \hat{j} + \hat{k}$ and $b = λ \hat{j} + 2 \hat{k}$ , $λ \in Z$ be two vectors. Let $c = a \times b$ and $d$ be a vector of magnitude 2 in yz-plane. If $∣ c ∣ = 53$ , then the maximum p …
JEE Main 2026View solution →
Let a vector $a = 2 \hat{i} - \hat{j} + λ \hat{k}, λ > 0$ , make an obtuse angle with the vector $b = - λ^{2} \hat{i} + 42 \hat{j} + 42 \hat{k}$ and an angle $θ, \frac{π}{6} < θ < \frac{π}{2}$ , with the positive $z$ -axis. If …
JEE Main 2026View solution →